Emergent gravity: positive and negative insights

A conference at MIT was dedicated to emergent gravity and I find the approaches of a vast majority of the participants (except for Subir Sachdev, who was talking about AdS/CMP) to this question unreasonable and hopeless; see the program and Backreaction for a report. As Moshe Rozali wrote, it is strange that no string theorists were invited, especially because many actual experts on emergent gravity were present in the same MIT building during the conference.



It is possible, and in fact likely, that the metric tensor - a set of fields introduced to physics by Einstein that define the spacetime, its dynamical geometry, and that underlie the gravitational force (because it results from the spacetime curvature) - is not a truly fundamental entity.

See also: Emergent space and emergent time (2004)

But it is very important to know some "details" how the gravitational force is actually supposed to emerge. There are two basic classes of approaches to the mechanisms of emergence:

• Preconceived, simple ideas that "should work" but they have never worked when their details were investigated (but people are often not ready to give up)
  
• Unexpected ideas that people didn't consider a few centuries or decades ago but that naturally emerged in some equations of physics and they actually do work (but people are often afraid to study them too much and to go too far from the old tracks)
  

Quite clearly, your humble correspondent denounces the first group while the second, mostly string-theory-based group is thought to be very important.

Very generally, different researchers and their teams may try different approaches. But their research should never stand on increasingly shaky and unlikely pillars. Every scientist may have a slightly different interpretation of the existing evidence. But his assumptions shouldn't become crazily unlikely: he should still rationally evaluate the available evidence. I will dedicate six more paragraphs to this sociological question, before I return to emergent gravity.

Some people say that different approaches to similar questions should be "supported" by the society. What they mean is that every scientist should try to assume whatever he wants, even if it looks extremely unlikely (and maybe even increasingly unlikely) given the available evidence, and bureaucrats or politicians are those who should ultimately regulate the number of people who study various approaches (via funding), probably depending on their P.R. departments.

I completely disagree with this kind of a "scientific method". If we talk about the real science, every researcher should individually try to obtain the right answers about the reality, instead of looking for biased answers, hoping (or claiming to hope) that his or her bias (or the bias of his or her team or community) will be compensated by others. Even when it comes to the very big questions - and, in fact, especially in the case of the big questions - scientists should try to evaluate the existing evidence as well as they can to decide which research approach they should choose. To do so, they must know at least something about the "competing" approaches. They should never leave the big questions to the bureaucrats or politicians because the big questions are a part of science, too (in fact, the most important one).

For example, it is foolish for a scientist to dedicate a whole life to an idea (with unspectacular consequences) if the probability that the idea is correct is much smaller than 10^{-10}, the inverse population of Earth.

Why? You can see that the contributions of such a scientist to science are likely to be negligible. How can you see it? Multiply his contributions by the population of Earth. This product now includes all the scientific work of mankind but it is still unlikely that at least one idea investigated by at least one person is correct. So even the expected value of the results obtained by the whole mankind would be pretty small: they would probably not find the correct theory in their lifetime. What one person is doing is 10^{10} times smaller so the value is really tiny.

It means that if scientists study pretty much the same problem - e.g. quantum gravity - they must be interested in all relevant arguments and evidence, instead of segregating themselves into different "fields". More concretely, loop quantum gravity is not a "different field" than string theory. Loop quantum gravity is the same field as string theory, namely quantum gravity - the only difference is that it is done by people who can't properly evaluate the scientific evidence and they end up with wrong answers. Unfortunately, they don't seem to care about real physics and real evidence whenever it shows that they're doing something incorrectly.

In the very same way, it is not true that string theorists should "isolate themselves" from the attempted alternatives. They should know what the alternative approaches are saying and they should have a qualified opinion about it. If they think that the alternative approaches are likely to be true or that they say something important, they should incorporate it in their work (or to completely change their approaches). If they think that the alternative approaches are simply incorrect, as I do, they should behave according to this conclusion, instead of being "nice" and support a wrong answer (and huge amounts of wasted man-hours and dollars paid to this hopeless approach). There is nothing "nice" about supporting bullshit.

Fine. Let me stop with sociology and return to the mechanisms of emergent gravity.

How space emerges in string theory

The oldest example began in 1919. Let me assume that the reader knows what the Kaluza-Klein theory is, at least at the level of Chapter 4 of The Elegant Universe.

Kaluza-Klein paradigm

In Kaluza-Klein theory, one can relate higher-dimensional theories to lower-dimensional theories by the trick (or mechanism) called compactification. There are two types of a description of a physical system in this context: the higher-dimensional one and the lower-dimensional one.

In the higher-dimensional description, one assumes that there exists a rather simple theory - for example, a field theory with a small number of fields - that is defined in a higher-dimensional space. In Kaluza's original example, a five-dimensional spacetime was equipped with pure Einstein's gravity.

The lower-dimensional example is "simpler" in one sense only, namely that the spacetime dimensionality is smaller. However, it has many more degrees of freedom. For example, in the original Kaluza-Klein theory, you need to Fourier-transform the five-dimensional fields over the fifth dimension. The individual Fourier modes generate a tower of infinitely many mostly massive four-dimensional fields. Their precise interactions are constrained - the infinitely many masses and interaction constants are linked to each other - because they remember their five-dimensional origin. So you can view this physical system as a four-dimensional theory but it is a special type of a four-dimensional theory, with infinitely many fields and infinitely many constraints on their properties.

Kaluza's original idea was to unify electromagnetism and gravity, the only two forces that the anti-quantum physicists of his era (such as Einstein himself) found worth studying. Qualitatively speaking, the idea worked - after the corrections by Klein who really realized and appreciated that the extra dimension was compact. However, using quantitative laws, the simplest version of the idea could have been ruled out rather soon. Note that the Fourier expansion is something that the ancient Greeks didn't understand well: it was only invented two centuries ago.

In string theory, the idea was generalized and a generalized Kaluza-Klein theory is compatible with several classes of realistic models of the real world within string theory. What are the generalizations? Well, first of all, the compact dimensions don't have to be a circle. They can be multi-dimensional shapes, such as the Calabi-Yau manifolds. The Fourier expansion has to be replaced by the expansion into the eigenmodes of some more general operators. More complicated shapes, such as conifolds, orbifolds, non-Kähler manifolds, warped throats, non-geometric compactifications, or many others have been studied and fascinating, coherent insights have been found in most cases.

But string theory has generalized the concept in many other ways that couldn't have been expected at the beginning. For example, the integer label distinguishing the different Fourier modes can have many interpretations. In the Kaluza-Klein theory, it has to be the momentum along the compact (fifth) dimension. In string theory, it can often be represented as a winding number or a wrapping number of strings or branes in a dual description.

Because of this unexpected property, new dimensions of space may emerge out of completely new phenomena. If there is a very short non-contractible circle in your compactification, strings can be winding around it many times. The winding number (how many times they're wrapped around the circle) becomes effectively continuous and can be reinterpreted as the momentum in a new dimension that becomes a new, large, effectively non-compact circle.

This phenomenon is called T-duality (and it can be rigorously proven in perturbative string theory). Compactifications on very short and very long circles are equivalent to one another once extended closed strings are allowed to wrap these circles. And they must be allowed to do so because an unwound string is always able to pair-create two opposite wound strings (as long as any interactions are allowed at all). T-duality can be applied to several independent circles in the stringy geometry: mirror symmetry is a remarkable example of a triple T-duality that relates two beautiful, but a priori unrelated six-dimensional Calabi-Yau shapes.

In principle, you could imagine that the whole three-dimensional space around us (let me omit time now; this limitation was discussed in the 2004 article) can arise from a conspiracy of many particle species in 0 dimensions. In this sense, the whole space is emergent. However, there are many ways how infinitely many objects in 0 dimensions can interact with each other. The knowledge of their higher-dimensional origin, or something equally constraining, is clearly necessary to find realistic quantum mechanical models in 0 spatial dimensions.

Just by saying that physics in 3 spatial dimensional is equivalent to a system in 0 dimensions, you haven't solved much. But indeed, we know several ways how physics of a field theory (or something that is approximated well by a field theory at long distances) in many dimensions can naturally be rewritten in terms of a theory in 0 dimensions. The BFSS matrix model is an example. However, we needed to know a lot about the higher-dimensional physics to find such a special model. Almost every "obvious" modification of the BFSS matrix model ends up with a quantum mechanical model without any higher-dimensional interpretation.

Holography

Holography is another, and perhaps even more famous example of emergent dimensions. In the case of Kaluza-Klein theory and its generalizations, we didn't have to rely on gravity. T-duality works even before gravity gets turned on. However, holography - the equivalence of a gravitational theory in D+1 dimensions and a typically non-gravitational theory in D dimensions - does depend on gravity very strongly. Why? Holography is related to the entropy bounds: the maximum entropy one can squeeze into a given volume is achieved by a black hole and the resulting maximal entropy only scales as the surface of the region, and not the volume as you might expect, in Planck units. And black holes need gravity to exist.

The anti de Sitter space is the most specific and successful realization of holography in action, because of Maldacena's AdS/CFT correspondence. The "bulk" of the anti de Sitter space is emergent here: we can describe its physics in terms of a theory that only lives on the boundary of the space (at infinity, in this case).

You might think that it is just another example of the Kaluza-Klein paradigm: we are making some kind of Fourier transform over the extra (radial, holographic) dimension. You might think that the boundary theory will have "infinitely many" fields of the Kaluza-Klein type. But you would be essentially wrong. The boundary theory is extremely simple - in the case of AdS5/CFT4 duality, it is a cousin of QCD: an ordinary gauge theory with a finite number of "elementary matter fields".

Now, the infinite tower of fields that we knew from the Kaluza-Klein case hasn't quite disappeared. You can still create infinitely many fields but they are composite fields. For example, excited strings in the bulk are created by various composite operators in the QCD, analogous to Tr(ZZZAZZZZB), the BMN operators. However, the very momentum along the holographic dimension is not encoded in this way. The reason is that the boundary theory is non-gravitational and it also includes off-shell, local Green's functions: you can study correlators of operators represented by Feynman diagrams where the external particles don't satisfy the expected energy-momentum-mass dispersion relations. However, the equivalent theory in the higher-dimensional bulk is gravitational and only knows about the on-shell scattering amplitudes. It is meaningless to ask about the local, off-shell Green's functions of the gravitational theory in the bulk: this fact is indirectly related to the holography itself.

Other mechanisms

Kaluza-Klein theory and holography are just two examples how dimensions may emerge - and transform into something else - in string theory. I should also be talking about topology transitions, quantum foam in topological string theory, deconstruction, and many other interesting mechanisms where dimensions of space emerge from something else. Gravitons themselves are emergent in perturbative string theory because they are closed strings in a particular vibration mode: see Why are there gravitons in string theory.

However, if I started to talk in this way, I would never stop because all of string theory may be viewed as a generalization of gravity that is emerging from something else. For example, all closed string modes may be thought of as components of a gigantic stringy "gravitational multiplet" and all other branes are generalizations of a string (and they can be dual to strings in various dual descriptions). There is no way to strictly separate "geometry" from "non-geometry" in string theory. This statement shouldn't be surprising because it is really equivalent to the fact that string theory unifies gravity with other forces (and matter).

But some people don't realize that these statements are equivalent because they assign similar propositions with emotional labels. Unification is good, so it should exist, but a separation of geometry from non-geometry is also good, they think. Well, it's no good because such a separation would be the opposite thing than unification and unification is good, indeed. ;-)

In string theory, all concepts we know are kind of linked to each other and all of them may be viewed as generalizations of geometry (a quantum, stringy geometry). Moreover, the combinatorial graph indicating how different fields, objects, and concepts in string theory are linked to geometry (and to each other) is not a tree graph. It has loops, too.

For example, the dualities (equivalences between various stringy vacua) link all the theories (and their objects) into a complex multi-loop network. Each loop implies a non-trivial prediction - a consistency check similar to the transitivity conditions for the transition maps on a manifold. And all these consistency checks have worked well, so far: they are almost as powerful as experimental tests in proving that this is a theoretical structure that a theoretical physicist simply has to care about. It is a beautiful, robust structure. And this whole structure may be interpreted as a generalization of Einstein's general relativity in which the right tools to generalize have been fully exploited.

So instead of talking about all ways how space (and time?) can emerge and transform in string theory, which is what all the conceptual efforts in string theory research (thousands of papers) are focusing on, even if they don't say so explicitly, let me return to the bad type of the research of emergent gravity.

Discrete and condensed-matter gravity

Some people are very impressed by the unexpected ways how macroscopic pieces of material can exhibit new types of behavior in condensed matter physics - superconductivity, superfluidity, Fermi liquid, highly correlated fermions, metals, fractional quantum Hall effect, and so on. I have surely missed some of the best examples.

I am also impressed except that Nature doesn't guarantee that similar ideas will work at many places. Some places need completely different ideas and we can often see what they are.

Other people talk about discrete physics, imagining that a finite volume of space is always made out of a finite number of easily visualized, "discrete" elementary building blocks. The space is a spin network and the spacetime is a spin foam (or a causal dynamical triangulation), they say. For some philosophical reasons, they find such a philosophical picture pleasing. But in physics, something's being philosophical pleasing is an entirely different criterion from something's being physically correct.

Assuming that something is only composed out of discrete blocks is a huge assumption - much like the assumption that a random, measurable, a priori real quantity will be integer-valued. It is very unlikely that it will be integer-valued. In the very same way, it is very unlikely that all of physics may be encoded in "discrete" quantities (even though, in some cases, both situations can occur - but there is usually a well-known argument, not just wishful thinking).

More concretely, these discrete descriptions of space suffer from a couple of very general problems. They almost always break the Lorentz invariance which is always a huge problem because the Lorentz invariance is one of the key experimentally verified principles underlying modern science (special relativity is crucial in particle physics). They violate the Lorentz invariance because the vacuum is not really "empty". It contains a new kind of luminiferous (or gravitiferous) aether. Consequently, one expects that a privileged reference frame is picked.

Moreover, the aether seems to have a huge entropy density - probably the Planckian entropy density if the building blocks have Planckian dimensions. Such a huge entropy carried by the vacuum would completely destroy thermodynamics (for example, it would cause a huge friction because such a "vacuum" resembles a highly viscous liquid) as well as interference in all interference experiments (because the microstates of the vacuum are distinguishable and they can't interfere with each other). It would also spoil the Lorentz invariance by itself because the entropy density is a time component of a four-vector (am entropy current) and its nonzero (huge) value is non-invariant under the Lorentz transformations, too.

For the typical composite theories of space, one can show that these problems are real and huge. The Lorentz violation in these theories is not "small" in any sense. Among many other problems, this bug also makes perpetuum mobile possible. ;-) The only method how to achieve a tolerable situation is to have a system whose vacuum can be shown to be fully equivalent to a traditional "empty vacuum" in a Lorentz-invariant field theory. If you can't see a reason why such an equivalent description should exist, it almost certainly doesn't exist and your composite theory is ruled out because it disagrees with some extremely basic features of our world such as the "emptiness" of the vacuum (e.g. the absence of friction in the vacuum).

There are other huge constraints that make similar composite models of a graviton impossible. The Weinberg-Witten theorem is a textbook example of these no-go theorems. These two extremely famous physicists have shown that composite massless particles with spin exceeding one cannot exist; in fact, even theories with an elementary particle with spin above one cannot be renormalizable local quantum field theories.

This result is a "negative" one in the sense that it kills someone's hopes. But I am among those who view negative results to be as important for science as positive results. Whenever we understand how Nature doesn't work, we also understand something about the way how it does work. These "negative" results usually lead to a reduction of research activity in a certain direction which is why many people don't like them. They steal "jobs" from the people. But this is not an objective, unbiased criterion. I think it is great if you can save man-hours in this way! If you get rid of the bias, positive and negative true insights are equally valuable.

Needless to say, in the real world, not quite all such man-hours are saved. Many people continue to investigate theories that directly contradict some of the known no-go theorems. The perpetrators usually don't understand the no-go theorems well. Most typically, they either ignore the theorem completely or they invent some bogus explanations why their theories shouldn't be subject to these no-go theorems (recall e.g. Garrett Lisi's bizarre "explanations" why he doesn't care about the Weinberg-Witten theorem).

If these people were sane, they would realize that their explanation why they "can" circumvent the no-go theorem could be used by the author of every single composite graviton theory (for example, everyone could say that at the end, they want to add a positive cosmological constant, which is a subtlety that Weinberg and Witten didn't take into account, they emphasize).

Consequently, it would follow that the Weinberg-Witten theorem is completely vacuous and the authors themselves, Weinberg and Witten, would have to be completely deluded. For some reason, the "composite gravity" geniuses don't see any problem with such an inevitable conclusion of their thinking. Now, the thing that irritates me is not that someone is ready to believe that Witten and Weinberg are deluded and that they write vacuous theorems. Feel free to believe so. But you are still wrong because the theorem is actually very powerful.

For example, the cosmological constant is completely irrelevant and you can see that it can't change the conclusion (that the composite graviton theories are ruled out). The vacuum energy only creates errors of relative magnitude 10^{-120} or so, altering the conclusions from the flat space. But the composite character of gravitons induces much greater errors - of order one - so they can't cancel. These problems - the cosmological constant and the compositeness - have nothing to do with each other.

I think that whoever tries to study similar "composite" theories should carefully read the Weinberg-Witten paper and learn their methodology. He or she should try to apply and modify similar reasoning for his or her context, too. And I assure you that it is not hard to modify the Weinberg-Witten arguments so that they can rule out every research direction in which the "gravitons" or the "metric tensor" are composite fields in the bulk of spacetime (that is however non-emergent).

String theory guides us to the right highway

String theory is able to circumvent the theorem in very unexpected ways, for example in the AdS/CFT correspondence. The reason why gravitons can be emergent or associated with composite operators is that it is not only the gravitons that are emergent: it is a whole dimension of spacetime (or more) that emerges, too. Such a broader process of emergence is harder to imagine a priori which is why people haven't tried it before the phenomenon was understood by string theorists (who tried to understand why some consistency checks concerning black hole entropy worked better than they expected).

So it is fair to say that most of the "very minimal" and "philosophically pleasing" pictures how gravity, geometry, and other things may emerge can be falsified. On the other hand, string theory exactly tells what kind of non-minimal extensions of these ideas you should pursue in order to have a chance that your theory won't be instantly ruled out.

There are lots of examples of this phenomenon - that string theory is able to "guide you" in finding many non-trivial and non-minimal mathematical structures and theoretical frameworks that share some features with the "cool and simple ideas" that you might invent after a few minutes but, unlike the cheap and fast ideas, these non-minimal ideas work. We can check that they do achieve what they claim.

For example, you may imagine that Cartan, Killing, Dynkin, and others wouldn't have been able to classify Lie groups and to find the exceptional ones. Nevertheless, string theory could have been discovered even without this insight. After a few years, they would also find the heterotic string theories and realized that one of their versions has 248 copies of a massless gauge field. They would be inevitably led to the E_8 group (and there are other constructions that are natural in string theory that lead you to E_8). Soon afterwords, they would discover the other exceptional groups as the subgroups of E_8.

There are many other, more complex examples of this kind that are behind the popular phrase that "string theory is smarter than us". For example, supersymmetry, a new symmetry that, morally speaking, circumvents the Coleman-Mandula no-go theorem (implying that symmetries that non-trivially mix the spacetime symmetries with the internal ones are impossible), was found in the context of string theory, too. It was sufficient for Pierre Ramond to try to incorporate fermions into the old bosonic string theory. He found both the superstring as well as the (worldsheet) supersymmetry.

Just like the experiments have often been necessary for the theorists to realize certain things that they could have discovered by pure thought (by they didn't), string theory is able to do the very same thing. It often helps us to search for a "needle in a haystack" even though we often find the farmer's daughter instead - i.e. we find a non-trivial, non-minimal construction similar to other constructions that have been looked at, except that the people were not able to combine all the right ingredients to make it work.

Even though Nature and string theory are demonstrably smarter than us, and smarter than Einstein and others, some people still try to be smarter than Nature and string theory. The only problem is that their attempts never work. The airplanes don't land. Virtually no interesting constructions - potentially relevant for Nature's mechanisms at the fundamental level - have been discovered in this way and most of the people who continue to investigate e.g. the emergent gravity - while the spacetime in their framework is not emergent by itself - are stuck with some excessively simple theories that have already been falsified.

Meanwhile, string theorists keep on finding fascinating new things, by making their careful "experiments" with string theory. These new discoveries have existed in the abstract Platonic world of cool mathematical ideas and they have only been "discovered". Certain people may feel happier if they "invent" completely new things except that this approach, while useful in engineering, hasn't led anywhere in theoretical physics. Nature can't be "invented". Its secrets already exist out there and we are only allowed to "discover" them. To do so, we must listen to Nature - through the experiments or string-theoretical calculations - in the right way to hear what She is trying to tell us.

You may try to be smarter than Nature but you will eventually fail because She rocks.

And that's the memo.

Sarah Palin & global warming

McCain chooses Palin as his running mate (playlist, 4 parts)



Sarah Palin (44), the governor of Alaska, and her life surely look fascinating and she will probably make McCain's GOP ticket much stronger (and certainly much younger! McCain is 72 today). She is a former beauty queen, ex-mayor, former sports reporter, hunter, shooter, fisher, wife of an Eskimo, pro-life feminist, mother of five, including a bundle of joy with XX+21.



But she's a great character.

There are all kinds of interesting things about her but because climate and energy policies are among the standard topics on this blog, I chose the video above. In this June 2008 Glenn Beck show, she talks about her lawsuit against the U.S. government that wanted to use the "endangered" polar bears as hostages to cripple her, Alaskan economy and to prevent them from tapping the resources, because of some unreliable climate models, as she calls them. She appears at 4:30, after an entertaining anti-environmentalist rant by Glenn Beck.

See also:

Palin not convinced on global warming (The Washington Post)
Palin: global warming not man-made (ABC News blogs)
Interview on McCain, abortion, climate change (NewsMax)

She has also serious doubts about Darwin's biology but I feel that alarmism is more serious a threat to the humanity these days than creationism. In the interview linked above, she answers the following to the last question about the impact of climate change on America and Alaska:

A changing environment will affect Alaska more than any other state, because of our location. I'm not one though who would attribute it to being man-made.

Oops, they just deleted Wikipedia's global warming skeptics category.

Bell Labs' fundamental physics research: RIP

Bell Laboratories decided to close their fundamental physics research.

Google News

That includes basic science, material physics, and semiconductor research. Because of short- and medium-term financial reasons, they will focus on networking, high-speed electronics, wireless technologies, nanotechnology, and software.

The discoveries made at Bell Laboratories, the research organization of Alcatel-Lucent, have shown the amazing creative power of the American commercial sector. Their achievements have led to six physics Nobel prizes, for

1. demonstrating the wave nature of matter (Davisson 1937)
2. transistors (Bardeen, Brattain, Shockley 1956)
3. electronic structure of glasses and magnets (Andersson 1977)
4. cosmic microwave background (Penzias, Wilson 1978)
5. laser-based cooling and trapping of atoms (Chu 1997)
6. fractional quantum Hall effect (Stormer, Laughlin, Tsui 1998)

Wow. Besides these rather fundamental breakthroughs, the Bell Labs have developed the radio astronomy, information theory, UNIX operating system, C and C++ programming languages, synchronous sound-motion picture system, long-distance transmission of TV signal, scrambled speech transmission system, photovoltaic cells, complex calculators, electronic music, WLAN, and dozens of other well-known things.



Century 21 calling: a 1962 Bell Labs promo film

It's sad that this powerful physics think tank will be gone. RIP.

CERN beats German LHC alarmists

It should be a trivial news that doesn't require any report except that in this crazy world, it does. ;-)

Court saves the LHC from Otto Rössler et al.

Boltzmann brains: popular misconceptions

Today, there are two anthropic hep-th preprints concerned with the so-called "Boltzmann brains". One was written by Bousso, Freivogel, and Yang, while the other was constructed by De Simone, Guth, Linde, Noorbala, Salem, and Vilenkin.

Many of them are big names, we like them, yet the papers are obviously wrong. Every individual sentence in the abstracts of these two papers actually seems to be incorrect by itself. The same comment applies to most sentences in the bulk of the papers. They use all kinds of wrong proportionality laws between the "volume" and the "probability" - the kind of laws that small pupils believe when they hear about the first proportionality laws in their science classes. Everything is proportional to everything else, isn't it?

Well... No, it's not. But let me start with some comments about:

Boltzmann brains

The entropy of a system never decreases "macroscopically", at least not "systematically" for long periods of time. This observation is called the "second law of thermodynamics", it underlies the so-called (thermodynamic) arrow of time, and using general methods of logic and statistical physics, it can be proven to hold in any physical system that admits macroscopic changes of the entropy: see the previous article about the second law.

And if the entropy does decrease for a while :-), the probability that such a thing occurs decreases exponentially with the total decrease of the entropy: when other things are "equal", whatever it exactly means, the probability goes like exp(-|entropy_jump|) which can be an impressively tiny number. Whenever you (approximately) say that the entropy is "macroscopic" (i.e. a large multiple of the tiny Boltzmann's constant, a number that is not too far from Planck's constant), it is effectively infinite in the natural microscopic units, and the probability of such an evolution is zero.

Still, the real entropy changes (locally, the entropy must decrease in some regions when we want to obtain life) needed to create e.g. a brain are finite so the probability is not strictly zero. If you consider a gas with a lot of hydrogen, oxygen, and carbon atoms, it's a messy, chaotic system. But there is some nonzero probability that the atoms in a square foot organize themselves in such a way that their positions and velocities are indistinguishable from the positions and velocities of atoms in a human brain that includes some particular memories.

Such a randomly created brain that is locally indistinguishable from a normal brain is referred to as a Boltzmann brain. Ludwig Boltzmann was the first man who played with these ideas: our life could have resulted from a random, very unlikely fluctuation of a high-entropy system towards a much lower entropy. Such an assumption would be, in fact, somewhat natural in a Universe that exists since t=-infinity.

Boltzmann, much like everyone else, realized that all the brains we have ever observed around are normal brains, i.e. results of well-known and canonical rules of evolution that takes place on a planet in the Solar System inside a Universe of the type that we know. More precisely, he knew that the entropy has apparently been increasing at least for hundreds of millions of years. Today, we know that it has probably been increasing for billions of years and because of the Big Bang theory, this time interval is likely to be the "whole story". The new biological and cosmological evidence has simply made Boltzmann brains unnatural and unlikely while orderly evolution became natural and likely.

Nevertheless, it is still possible, at least in principle, for brains that are locally indistinguishable from ours to be born in a complete chaos, by an unexpected entropy drop but without all the complicated evolution.

That's a fun game except that many people recently started to say that such games can actually constrain possible models of cosmology. Of course, they can't and any framework of ideas that claims to rule out a cosmological model by counting some Boltzmann brains can be falsified by itself. Most of the anthropic researchers, including the well-known cosmologists, seem to share a couple of childish, elementary misunderstandings about the character of Boltzmann brains and all these myths are crucial yet shaky pillars of the anthropic papers. Let's look at them and try to correct them.

Myth: the Boltzmann brains immediately turn into chaos

This myth arises because its advocates probably don't understand quantum mechanics well enough and they inconsistently mix several interpretations of quantum mechanics, to achieve nonsensical conclusions. To see what actually happens with Boltzmann brains in one second, let us begin with classical physics.

In classical physics, we really talk about the positions and velocities of all the atoms inside the Boltzmann brain. If electromagnetic waves inside the brain are important for its identity and memory, their configuration in a Boltzmann brain must reproduce a normal brain, too (by definition of a Boltzmann brain).

But as we know, the laws of physics are pretty much local. So if we know that the normal brain will be thinking at least for a second or so, until the signals from the exterior influences manage to propagate inside, it follows that the corresponding Boltzmann brain will be doing the same thing. The same initial conditions in a region imply the same results!

Of course, the environment in which a Boltzmann brain lives will influence its future evolution. If a Boltzmann brain is placed in the vacuum or some light gas, the subsequent evolution will bring him or her the same sensations as the feelings of a normal brain of a person who just appeared under the guillotine in the critical moment. I haven't tried it ;-) but whatever you feel, the evolution of a Boltzmann brain and a normal brain will be qualitatively identical. The positions and velocities of the atoms of brain evolve in the same way while the external conditions only begin to influence the internal structure of the brain after much longer intervals than the typical intervals needed to make a few operations in the brain.

If a Boltzmann brain is equipped with a full-fledged Boltzmann body, chances are that it will survive for several minutes, before it or he or she suffocates. ;-) If you begin with a Boltzmann brain supplemented with a Boltzmann body inside a properly isolated Boltzmann hotel equipped with Boltzmann food and Boltzmann toilets (inside a chaotic Universe), it or he or she can happily live for 70 years or more. Such a life will be pretty much indistinguishable from the life of a normal brain.

This conclusion should be obvious in the classical setup because everyone can imagine the differential equations that dictate what happens with the atomic coordinates and momenta: identical initial conditions will lead to the same outcome. But it is a "macroscopic" conclusion that is guaranteed to be shared by quantum mechanics, too (because quantum mechanics reduces to classical physics for similar macroscopic questions). However, the anthropic people often incorrectly say that their Boltzmann brain is instantly transformed into chaos.

Their mistake follows from an erroneous interpretation of the phrase "quantum fluctuation".

They essentially use this phrase in the same way as we normally do in Feynman's path integral approach to quantum mechanics: we sum over all histories and most of them are "chaotic". But the fact that one of these chaotic histories looked like a Boltzmann brain at t=0 isn't enough to say that the system was found in the state of a Boltzmann brain at t=0. These are entirely different things.

If we say that the initial state looked like a Boltzmann brain described by a wave function, psi, at t=0, it means that the path integral should be organized as a sum over all histories with various given initial conditions at t=0, weighted by the wave function (or functional) for each initial condition. When you do so properly, the local predictions will, of course, be independent of the question whether the brain "is" a normal brain or a Boltzmann brain. Physically, it's the same brain, after all.

So it is wrong to expect that Boltzmann brains would behave completely differently than normal brains. Because of the universal, local laws of physics, they behave in the same way. The greater volume we decide to arrange properly, the longer time will be needed to observe any difference between the situation of a normal observer and a freak observer.

Moreover, it doesn't matter whether we think about these issues in terms of classical physics or quantum physics: a full measurement of a complete set of observables - i.e. a full identification of a wave function - leads to equally "specific" initial conditions as in the case of the classical initial conditions. Quantum fluctuations do influence the evolution of physical systems, according to quantum mechanics, but the influence is identical for normal brains as well as Boltzmann brains. Once a Boltzmann brain is defined by initial conditions at t=0, to reproduce a normal brain, their physical properties will be indistinguishable for positive t, too.

Truth: Boltzmann brains have a genuinely nonzero probability to emerge

Because the volume of spacetime is "infinite", the anthropic people imagine that it is enough to "beat" the smallness of the probability density that a Boltzmann brain occurs in a region. Because the probability density is nonzero, it is guaranteed that infinitely many Boltzmann brains occur in the whole spacetime.

Such games involving indefinite products, such as zero times infinity, are subtle and one shouldn't be as naive as Zeno when he was designing his famous paradoxes. In the real world, there are actual cutoffs that imply that infinite things are not quite infinite. This is true for the infinite volume of spacetime, too. However, we will see that the conclusion - that the large volume wins - is correct, anyway.

To be very specific, let us try to construct an actual realistic brain from the thermal quantum fluctuations in our (asymptotically in the future) de Sitter space.

If the temperature of the space were exactly zero, a brain would never be spontaneously created. This is a special case of my previous comment that "quantum fluctuations" are not able to do certain things that the anthropic people incorrectly imagine. If the Universe is known to be in the vacuum state, i.e. the eigenstate of the Hamiltonian with the minimum eigenvalue, it will be in the same vacuum state forever. With probability one: for sure. The vacuum state itself "includes" many quantum fluctuations (complicated trajectories contributing to the path integral; or non-trivial wave functionals with nonzero chances to have nonzero velocities) but it is exactly stationary.

So we really need some "chaotic material" to create the brains randomly. The de Sitter radiation from the horizon can play this role. But its temperature is really tiny: the typical thermal wavelength is proportional to the size of the Universe, about 10^{60} Planck lengths. The temperature is therefore 10^{-60} in Planck units. We need to create an elementary "electroweak" particle whose energy is something like 10^{-30} Planck energies. The Boltzmann factor, exp(-E/kT), adds a huge exponential suppression. In this case, it is exp(-10^{-30}/10^{-60}) = exp(-10^{30}).

Now, you should create 10^{27} different, a priori "independent" elementary particles (the number is related to Avogadro's constant: let's neglect the interactions, hoping that they don't change the result qualitatively), to construct the whole brain. So in order to obtain the combined probability for 10^{27} "independent" events of the same type, you need to take a huge power of the previous tiny probability, exp(-10^{30}): the exponent in this new power must be 10^{27} itself. These are very tiny numbers and we are combining the powers in too many confusing ways so let us write a displayed formula:

exp(-10³⁰) ^ (10²⁷) = exp(-10³⁰ x 10²⁷) = exp(-10⁵⁷).

This is a similar supertiny, expo-exponential probability to the previous one, with the expo-exponent of 30 replaced by 57. ;-)

This probability may look ludicrously small and it indeed is. But the huge volume of spacetime is still sufficient to beat this tiny number. I haven't told you but the volume of spacetime shouldn't be thought of as an infinite number: instead, you should think that the maximum age of the Universe is the Poincaré recurrence spacetime volume, exp(10^{120}) in Planck units, where 10^{120} is the estimated maximum entropy in our Universe (given by the area of the de Sitter horizon, which goes like the radius, 10^{60}, squared): the actual entropy of the "interior" of our Universe today is only 10^{100} or so. After this very long time, exp(10^{120}), the Universe tends to "repeat itself", if we simplify the situation a bit. You shouldn't believe that longer time intervals are "independent".

So if you multiply the "nearly infinite" spacetime volume, comparable to exp(10^{120}), by the tiny probability density to create a Boltzmann brain, exp(-10^{57}), you still get something like exp(10^{120}-10^{57}) which is still essentially exp(10^{120}). The volume wins. It is no coincidence that the number 57 was smaller than the number 120: whenever the "brain" fits into the Universe, your exponents will be sorted in the same way. So does it mean that even a simple de Sitter space with an infinite future predicts that "you" should be a freak observer inside an incoherent, chaotic Universe? Can this simple and universal counting falsify an ordinary de Sitter cosmology?

The answer is, of course, "No". It was the probability density for a brain creation itself, around exp(-10^{57}), that determined the "importance" of the effect of a spontaneous brain creation. If we multiply this small number by a huge volume, we obtain a huge result that has no physical relevance for any place of the Universe in the present, past, or future (because the factor of the "spacetime volume" transformed the quantity into some "statistics of events in the whole spacetime" i.e. a global quantity which can't possibly influence any observable phenomena in a region of spacetime, by locality and causality).

Nevertheless, many people say "Yes, the huge number of Boltzmann brains in the whole spacetime volume rules out even an ordinary de Sitter cosmology (and many others)". Their incorrect "Yes" answer is partly built on another:

Myth: physical initial conditions are defined in terms of brains

To be specific, let us consider a looming collision of two planets. We know that they're going to collide and our task is to predict how many big pieces will be created.

The anthropic people think that the initial conditions of this physics problem involve a brain that was just informed about the coordinates of the colliding planets and physics should be able to predict what the mouth, connected to the brain, will say after new observations following the collision that update the brain's knowledge. ;-) So they formulate the problem in the following way:

Input: Brain, connected to eyes, sees two planets
Desired result: What will it see after the collision?

But that's actually not quite the same problem as physics is ready to solve. It may sound counterintuitive to the anthropic people ;-) but the problem above belongs to psychology, not physics. Physics defines the initial conditions and the questions in a different way:

Input: Two planets actually exist at some points of space
Desired result: What will their material do after the collision?

Now, I will assume that the reader believes me that it is the latter, objective formulation of the problem that physics would actually like to answer. The previous, subjective formulation can perhaps be a good proxy. It is a good reformulation of the physical problem assuming that it is equivalent. But is it really equivalent?

Well, the answer obviously depends on the quality of the instruments that measure the state of the planets before and after the collision, including telescopes, eyes, preprint servers that collect the data, and brains. ;-) If at least one of these players fails to faithfully reproduce the reality and transmit the real data, physics of planets will have (almost) nothing to say about the perceptions of a particular brain.

If the telescope is actually directed at a science-fiction movie on TV, if the experimenter is drunk, if the preprint server is hacked, or if one of these important people who transmit the data from the telescope to the theoretical physicist is an imbecile, which is often the case, the theoretical physicist will clearly be unable to make good predictions about the future observations extracted from the telescope. ;-)

Even if someone defines the "psychological" physical problem insufficiently accurately - for example, he is only careful to define the initial state of some neurons (or atoms) but not others - the result is the same as it is for a lens (in the telescope) with too many cracks or a microprocessor (owned by the preprint server) with too many burned transistors: the link between the actual physical phenomena (involving the planets) on one side and the perceptions of the brains (that try to observe the phenomena) get disconnected. Physics of planets will have nothing to say about the brains. The correct predictions of the "brain problem" will depend on the precise character of the cracks, unknown or missing neurons, or burned transistors.

Now, I am convinced that when the situation is described in these clear terms, every sane person will agree with me. Nevertheless, it seems that the anthropic people often seem to implicitly disagree. I guess that they feel uncomfortable about the fact that physics talks directly about the planets even though the perceptions of our brains are the only "real" physical phenomena that actually inform us about the initial and final conditions of physical systems.

Well, I agree with that. Even though we usually imagine that the real world "objectively" exists, we always learn the "objective" information about it in some indirect ways that include the brain cells. But as my presentation indicates, the situation of a Boltzmann brain is pretty much equivalent to the situation with a fake telescope or a very drunk astronomer (for pedagogical reasons, I avoided drugs in this explanation). There's nothing really mysterious about it. But we could still ask:

Why are most of the brains we observe working well?

In other words, why are they normal brains? The first obvious answer is that they are not. ;-) Fine. But it still seems that the percentage of brains that work pretty well is much higher than the tiny percentage in the hypothetical ensemble dominated by Boltzmann brains. Is it a paradox or an observation that deserves a nontrivial dynamical explanation?

It's certainly not a paradox for me. First of all, it's not shocking that all observed brains are normal if at least one of them is. This proposition largely follows from the definition of a normal brain. A normal brain XY is a brain found inside a Universe where large entropy decreases don't appear more often than predicted by the second law of thermodynamics, including the microscopic fluctuations, and where the evolution largely follows the known dynamical laws.

If a brain XY has a Boltzmann brain somewhere in its vicinity - for example, on the same planet - it proves XY cannot be a normal brain either. This conclusion follows from the definition of a normal brain in the previous paragraph. A single Boltzmann brain is enough to prove that the whole setup and the whole planet is a "fraud". Whether a brain is a normal brain or a Boltzmann brain depends on the environment.

So if someone is trying to pretend that the Boltzmann brain paradox becomes more serious whenever we observe another Boltzmann brain, i.e. when the number of normal brains is very large, he is incorrectly assuming that the Boltzmann vs normal character of two or many brains are independent questions. They're not independent at all. Either the whole planet is a fair evolutionary setup with normal brains only, or the whole planet is fraud and all of its brains should be called Boltzmann brains.

Because of this simple reason, it is enough to understand why at least one brain on Earth is a normal brain. For me, it's most natural to consider my own brain. I recommend you to use yours if you want to reproduce the deduction below. ;-) Of course, I will find out that my brain is almost certainly a normal brain which is also why I can trust that it reproduces the data about planets (and other objects) well. Let us show both methods to determine whether my brain is a Boltzmann brain: the sane (a.k.a. scientific) method and the anthropic method.

Is my brain normal? Anthropic method

According to this method, my brain must be a generic brain in the ensemble of objects that look like brains in our de Sitter spacetime (assuming that this is the right cosmology). How many conditions a piece of material has to satisfy in order to be called "my brain" (especially how large a region around the brain must coincide) is never determined but despite this cutoff dependence, the anthropic people believe that the number of Boltzmann brains is physically relevant, anyway. (It's not!)

There are about exp(10^{120}) of such brains - within one Poincaré recurrence 4-volume - and virtually all of them are Boltzmann brains. Because there is a full democracy between these brains, the anthropic people think, those Boltzmann brains win. So I must be a Boltzmann brain, too.

Note that this approach is politically correct because each piece of organic junk somewhere in the future chaotic dumping ground of noise is on par with a human being only because it looks similar. These pieces of junk don't have to thermalize, fight, or find a support of the Pentagon or the Kremlin. They're there so they immediately and eternally have all the rights and if you say that they're just pieces of organic junk, you are being politically incorrect and, according to the anthropic "science", you are even wrong.

Well, that was funny but let us now use a normal brain, and not a freaky one, to determine whether my brain is normal or freaky. ;-)

Is my brain normal? Sane method

First, we must understand what the question actually means. What does it mean for the brain to be normal? It is a question about the whole Universe: does the Universe surrounding my brain satisfy the laws of physics, including the second law of thermodynamics at macroscopic scales?

More precisely, we ask whether it has satisfied them in the past. Why? Because in the future, unless we make insanely unlikely assumptions about the present, the second law of thermodynamics will automatically hold. So we are really asking:

Is/was the history of the Universe surrounding my brain compatible with the (macroscopic) second law of thermodynamics?

This is the only way how one can refine the original question so that it is well-defined.

At this moment, it is crucial to notice that this is a question that assumes - and must assume - something about the present (the existence of a brain at t=0) and that wants to deduce something about the past (e.g. validity of the second law). So it is a textbook example of a retrodiction. In quantum mechanics, the future probabilities can be calculated "directly" from the squared complex amplitudes but, as has been explained many times on this blog, e.g. in the article called Bayesian inference, retrodicted probabilities can never be equally canonical or unique and they always depend on priors.

In this particular case, I am trying to decide whether my brain is normal or a Boltzmann brain, as clarified above. These are two hypotheses. At the beginning, I must choose some prior probabilities for these hypotheses. A fair and rational treatment always gives a nonzero chance to every qualitatively distinct possibility. So I choose the priors to be 50% for a normal brain, 50% for a Boltzmann brain.

Now, I can collect some evidence: the data can be used for logical inference, to refine the probabilities that the two competing hypotheses are correct. So I observe a few macroscopic phenomena in the world around me. For example, I observed that two eggs were broken but no egg was unbroken. The probability that this is what happens with the eggs according to the normal brain hypothesis is essentially 100%. The probability that such a thing occurs in a Universe near equilibrium, without a well-defined arrow of time, i.e. in a Universe where every change of the entropy is just a fluctuation, is something like exp(-EntropyIncrease) which is really tiny, something like exp(-10^{27}). Most likely, different pieces of the eggs should have increased or decreased their entropy pretty much randomly.

So the evidence has brutally disfavored the Boltzmann brain hypothesis. It is obvious that we can easily perform a few macroscopic measurements that can make the posterior probability of the Boltzmann brain hypothesis pretty much as low as we want. The only alternative hypothesis, the normal brain hypothesis, is thus proven beyond doubt. Instead of eggs, it may be more conceptual to observe the standard evidence of evolution and the Big Bang cosmology: this standard evidence implies that it is extraordinary likely that our brains are results of evolution in a normal Universe with an increasing entropy i.e. that they are not Boltzmann brains.

If someone obtains the opposite answer, namely that our brains should almost certainly be Boltzmann brains, he is clearly making a mistake because the scientific evaluation of the available evidence and of the existing theories can't lead to two profoundly different figures for the probability. For example, if Roger Penrose argues that the Big Bang couldn't have been at the beginning because low-entropy states are always unlikely, the evidence simply disagrees with his theory. He may impress the Hard Talk host with huge numbers like exp(10^{120}) but if he uses the numbers incorrectly, the value of his argument is zero, anyway. In a children's game where you win if you say the largest number, he could win. But in science, he can't.

My setup is self-consistent, consistent with data, compatible with all the conventional (as well as slightly less conventional but conceivable) cosmological models, and pretty much complete. It implies that the Big Bang expansion and the evolution of species almost certainly did take place; so it means that every derivation that concludes that the Big Bang expansion and evolution didn't occur and that our brains are Boltzmann brains has to be wrong.

Indeed, my conclusion means that our brains are very far from being "generic" in the (almost infinite) set of all physical objects that look like our brains in our de Sitter spacetime. But this "non-genericity" can be easily shown - and has been easily shown - to hold: one macroscopic observation is enough to settle the question. There is nothing wrong with this non-genericity. The same evidence that supports evolution and the Big Bang theory also falsifies all theories and all "philosophies" that either assume or imply that our brains should be generic in the whole de Sitter spacetime. The genericity hypothesis is simply falsified by extremely robust and universal arguments.

If you don't like that I needed an observation (to see an increasing entropy of eggs or some evidence of evolution or the Big Bang expansion), let me repeat that it is impossible to "predict" the probability that my brain is a normal brain without making any observations simply because the "prediction" of the Boltzmann/normal character of our brains is actually a retrodiction and retrodictions always heavily depend on priors (assumptions about the past): and there are no canonical, universal priors in Nature.

One always needs to make some assumptions about the history which was surely affected by some "random" events whose existence is implied by the probabilistic nature of quantum mechanics. Some conclusions (some retrodictions) heavily depend on the history and the priors, others don't, depending on the context. But experimental data are always needed to reduce this dependence.

In this logical framework of inference, which is the only rationally justifiable way to make similar retrodictions about the Universe around us, it was trivial to show that my brain, and therefore all brains on Earth, are almost certainly (mostly) :-) normal, non-Boltzmann brains. This conclusion didn't depend on any detailed features of the cosmological model that governs our Universe.

So I have proven that my brain is "normal" in all cosmological models we have considered. It follows that any argument that allows to rule out a cosmological model by considerations involving the Boltzmann brain paradox has to be wrong: by the simple but careful argument above, I have falsified all such theoretical frameworks. In other words, if you combine my general physics considerations and facts with the assumption that implies that our brains are almost certainly Boltzmann brains at least in one conceivable cosmological model, you obtain an inconsistent system of axioms. So you should better be careful and not to add anything that creates such an inconsistency. The culprit is, of course, the anthropic reasoning itself.

We may be missing some extra "laws" or "axioms" about the initial conditions, vacuum selection, and similar stuff but if you try to add "genericity" or some related anthropic axioms to the dynamical laws we (roughly) know, you are just adding "too much" or a "wrong thing". The combination is inconsistent.

The anthropic methods to deduce that a theory predicts that we should be actually Boltzmann brains, given certain cosmological data, are simply irrational and wrong. They reject basic rules of logical inference and replace them with wrong, unjustified, and unjustifiable proportionality laws between quantities that are not proportional in any sense, namely the probability that "we are something" and "the number of somethings in the spacetime". These incorrect proportionality laws are the infamous "genericity assumptions".

I believe that this "selection fallacy", assuming that objects must be "generic" in some randomly chosen class of similar objects (that share some properties but not necessarily others), is ideologically driven. Those people believe that everyone is "equal", where "everyone" depends on the current fashionable conventions and "equal" should even influence the probabilities that different people have different properties. The Boltzmann brains are able to get into their ensembles so they are equal, too: it would be a form of racism to think that Boltzmann brains are just irrelevant pieces of organic junk somewhere in an irrelevant, extremely distant future, wouldn't it?

But such an equality between different elements of a set only holds physically in extremely rare situations, namely when there is a mechanism that "enforces" the equality of the whole class of objects that share some particular properties. For example, different microstates of a gas are (almost) equally likely because of thermalization - that needs all the degrees of freedom of a closed system to interact with each other for a sufficiently long time. Thermalization chaotically probes all possible microstates - or places in the phase space - so all of them are "equally likely", after some time (as the ergodic hypothesis explains).

Analogously, citizens of a democratic country may have "equal rights" in many respects if there are police, army, or courts that enforce such an equality. But if there is no mechanism that enforces or otherwise guarantees the "equality", the equality simply doesn't exist physically (and such an equality often contradicts some of the real laws of Nature that can be determined otherwise). If you imagine that people have God-given human rights or God-given equality with all other people, you are free to imagine that but your imagination will have no physical consequences because it has nothing to do with physical reality, at least until you take over all armies in the world. Until you do so, cannibals can still easily eat you in Oceania. If we knew trillions of aliens, you wouldn't even be sure who can be counted as a human being. These questions clearly depend on social conventions and they can therefore have no immediate impact on physical phenomena or correct physics calculations.

In this most extreme case of Boltzmann brains, a piece of organic junk can emerge in the year exp(10^{120}) somewhere in the middle of de Sitter chaos. This piece of junk can look like my brain and there can be googolplexes of such brains but their existence will influence neither my rights at the present time nor rational calculations of physical phenomena that involve me. In fact, both of these influences would be not only unjustified but even acausal. Everyone who assumes otherwise is deluded and the probabilities in his papers are wrong by a factor of exp(10^{120}) or so which is a pretty bad error: an exponentially worse error than one that leads to the cosmological constant problem that some people wanted to be solved. ;-)

And that's the memo.

Long-term predictions and wishful thinking

I was trying to understand the ideological framework that leads so many people in the West to dismiss Russia as a "country in decline" exactly at the moment when it's rising from its knees, regaining its lost self-confidence, and surpassing the world in the GDP growth as well as in its military flexibility and readiness.

It seems that this ideological framework is a conglomerate of at least five general fallacies that also appear in many other contexts and that I would like to analyze. The only "objective" comment against the impressively good and promising condition of current Russia that I have fully understood is its negative population growth. Well, in 2007, there were 11.3 births per 1,000 people in Russia, more than 10.7 in the U.K. but less than 14.2 in the U.S. At any rate, there's not much difference here. Because of the lower life expectancy, there are more deaths per 1,000 citizens in Russia. But all these numbers, especially the birth rate, are flexible and can change.

However, the critics of Russia seem to be certain that in 2050 or so, Russia will be going down. Moreover, this idea influences their opinions about the "right" behavior that the Western politicians should adopt today. Fine, so let me first enumerate the (corrected) fallacies, before I will discuss them in detail, together with many other examples of these fallacies:

1. It is irrational to try to predict demographic subtleties in the very long run, e.g. in 2050
2. Even if it were possible to predict these things, they shouldn't significantly influence rational decisions in 2008, especially not our "perception of justice"
3. Even if the trends in 2050 could be predicted, it is irrational to assign them with positive or negative moral labels
4. Even if a quantity could be expected to be in "decline", it surely doesn't mean that you can imagine that it will be zero any time soon
5. When a rational person applies a certain kind of predictive methods and assumptions to one nation (or other subjects or objects), he should do so consistently with other nations (or subjects or objects), too.

Fine. So let me discuss these issues in detail.

1. Very long-term predictions are irrational

The most obvious example of this fallacy is global warming. Certain people want to plan the society up to the year 2050. In fact, the next IPCC report will want to prepare plans up to the year 2300. The latter number displays lunacy that is 70 times higher than the lunacy of megalomaniacs such as Iosif Vissarionovich Dzhugashvili who had 5-year plans only.

The society is so complex that it is unreasonable to make reliable or even semi-reliable predictions into a future that is as distant as the year 2050. What will be the relevant questions for the society in 2050 is almost completely unknown today. To see that it is the case, just look 50 or 100 years into the past: could the people who lived then be wisely planning our lives or to realistically expect what we would be talking or worried about?

I am convinced that every sane person must be able to see that the answer is clearly No. The typical time scale where the key "fashionable" problems of the society mostly change is comparable to 5-10 years. There are many other questions that don't change so quickly - for example, the qualitative patterns of planetary orbits don't change for billions of years - but the humans are rather unstable, constantly changing physical systems. There are general aspects of the human behavior that do not change for centuries; but there are many more fashionable things that change in a few years.

2. Very long-term predictions have nothing to do with current decisions, anyway

Even if it were possible to predict how the society is going to look like in 2050 or 2300, such a vision cannot influence the decisions in 2008 as long as the latter are rational. The impact of a particular decision made in 2008 on events in 2050 or 2300 is both uncertain and tiny in average. The reason why it is uncertain is that the society is a very complex system and the consequences of a decision that we can make right now will be "thermalized" - i.e. challenged, compensated, and overcompensated by many, often deliberately opposite decisions in the future.

From a human perspective, 50 years or 300 years are extremely long time intervals. Many more decisions and their revisions will be made between 2008 and 2050 and choosing decisions in 2008 according to their impact on the life in 2050 is a demonstration of someone's inability to see the difference between different time scales. Decisions about XY should only consider the future YZ years where YZ is the typical time scale at which XY is changing - for example measured by the time scale at which things similar to XY were changing in the past. For political things, the time scale is comparable to 5 years and is not far from the time scale at which a politician has the credentials to change something.

3. If something is likely to happen, it doesn't mean that it's a good thing, and vice versa

Americans are the best examples of optimists. Optimism means to believe in a high positive correlation between the future events that we consider "good" and the future events that we consider "likely". Pessimists have the opposite correlation and the people who rationally realize that there's no clear correlation between "good" and "likely" are called realists. ;-)

How does an optimist achieve such a correlation? Well, there exist two basic methods. Either he looks at the things that are "likely" to happen, according to his estimates, and he decides that they are pretty good: if we exaggerate a bit, such an optimist simply accepts the future, whatever it is. These optimists suffer from "lethargy" but they can live with it happily.

The other possibility is that the optimist looks at the things that he considers "good" and decides that because they are good, they must also be "likely" to happen in the future. We say that this subgroup of the optimists suffers from a fallacy called "wishful thinking". For example, feminists may decide that it is "good" for the percentage of women in physics to increase (because of their irrational ideology), and because it is good, many of them also decide to believe that it is a likely outcome (which is a combination of two irrational steps).

Incidentally, the pessimists fall into these two basic groups, too - even though we usually don't speak about these subtleties. ;-) Recall that pessimism is a belief in a high correlation between events that are "bad" and events that are "likely". A pessimist may suffer from a "reverse wishful thinking": because something is bad, it is likely to happen, he thinks. Most of the pessimists who display reverse wishful thinking have an agenda because the "bad" thing is actually a very good thing for them personally: most typically, the "bad" outcome could help them to show that they were always right that something sucks! ;-)

There also exists the other type of pessimists. They think that because something is likely to happen, it must be bad. These people are "inherent grumpy sourballs". For example, Peter Woit knows that the percentage and relative importance of string theory in theoretical physics is going to increase, so it must be a bad thing. :-)

A realist doesn't believe either of these fake correlations: a future event can be likely or unlikely, good or bad, and there is no good a priori reason for a correlation between these two types of adjectives. The realist's position is clearly the most rational one but that doesn't quite mean that the realists always have the highest survival advantage. I believe that in the long run, it is probably healthy for individuals to be optimists. If you know about contexts where the pessimists have a systematic long-term advantage, I would love to hear about them.

Besides the optimism/pessimism question, I would like to stress that a falling population of Russia, even if it continued, is not a "moral vice".

4. An increase or a decline is something else than a catastrophic increase or a catastrophic decline

Another very frequent fallacy is to identify a "nonzero trend" with a "catastrophic trend". A nonzero positive and negative trend is something that is almost guaranteed to be observed for every quantity we can imagine. On the other hand, a catastrophic positive or negative trend is something very unlikely that only appears in exceptional cases. Many people believe that if they demonstrate that a quantity is not going to be constant, they have also proven an imminent catastrophe. Instead, they have only proven an inconsequential truism.

Again, global warming is the most obvious example. The fact that the average temperature on Earth has been changing and is likely to change by 2300 is often interpreted as a global catastrophe. Needless to say, these are very different things. There are often up to 123 orders of magnitude of difference in between these two possibilities. The vacuum energy density is positive and one could reasonably expect it to take the catastrophic, Planckian proportions that would be enough to kill even every single proton. ;-) However, the real, observed vacuum energy density is smaller by 123 orders of magnitude and it is harmless for life.

Some people only use the "continuous" thinking for a while but once they see that something is nonzero, they adopt a "discrete", black-and-white thinking in which a positive value is the same thing as a divergent catastrophe. It is not the same thing. For example, the 0.6 °C of warming that can be expected by 2100 will be as harmless as the same warming during the 20th century. To get a more decent weather on most of its territory, Russia would need a warming by 15 °C or so. ;-)

In the case of demographics of Russia, the opponents of Russia, after they (irrationally) decide that they have proved that Russia's population will be declining by 2050, seem to conclude that Russia will effectively absent and it shouldn't play any role, not even today. You see that this reasoning unifies most of the fallacies discussed in this article: irrational long-term predictions, a wishful thinking, a wrong identification of the interpretation of quantities in 2008 and 2050, and many others. One of the fallacies is that they think that if the population of Russia is going to decrease, it is effectively zero.

But even if the population of Russia decreased from 140 million to 120 million by 2050, it will clearly fail to change any qualitative features of the discussion about the role of Russia in the world. The GDP per capita or the military power per capita may change more dramatically (especially if the oil price is going to increase) so that the population decrease will be overcompensated. Moreover, you don't know what will happen with the population of other countries, either.

The only known possible way for a mad politician to be able to "forget" about a large nation altogether has been a "final solution". Unless you want to repeat something along these lines, be sure that Russia will be an important player on the international scene for the decades to come.

5. Analyses of situations in the world should be self-consistent and follow unified rules

This brings me to the last point: consistency. That's an immensely important value for (good) theoretical physicists. A theory should be both internally self-consistent, i.e. to predict a unique answer to each well-defined question that belongs to an a priori allowed interval, and the theory should also be used consistently for all relevant phenomena.

If someone proposes a new physical law, he must insist that the law should be good for the description and predictions of a whole, well-defined class of phenomena. By the adjective "well-defined", I mean that the boundaries between the phenomena where the law should be trusted and those where it doesn't have to work should be known, at least approximately.

If a hypothesis disagrees with an observation of a phenomenon in this class, it is falsified. Sometimes, it is enough to change the definition of the "class" where the hypothesis should hold i.e. to make a more modest claim. However, in many cases, it is impossible and the hypothesis must be simply abandoned. For example, a "theory of everything", i.e. a hypothesis about the dynamics that governs all fundamental forces and particles in the Universe, should be valid universally. It follows that every disagreement of such a candidate theory with a (correctly made) observation means that the candidate theory is instantly falsified.

If you can only choose a few hints, a few cases where your theory looks OK, but you have to neglect its other, bad predictions - typically predictions that are obviously wrong even without any detailed measurements (e.g. anomalous or divergent ones or negative probabilities) -, it is simply not good enough as a starting point for a candidate theory.

In the case of the population growth, the critics of Russia clearly don't look at the world consistently. China has had a one-child policy to regulate its population growth (which was still positive). However, it is clear that new conditions and policies can change many things. For example, the population growth in the Czech Republic used to be negative a few years ago, too. That's no longer the case. Long-term predictions of such dynamics is impossible because it will be affected by all kinds of factors, including the individual psychology of typical citizens, the national wealth, migration, and government's policies.

If we look at Russia from different angles than the population growth, we find many other examples of inconsistencies. For example, a commenter has hysterically criticized Russia for having signed the Kyoto protocol. That doesn't look like a consistent criticism given the fact that 181 other parties have ratified the protocol, too. ;-)

The same comment applies to Russia's recent successful operations in the Caucasus. It may look cute to someone to criticize Russia for these things except that NATO has done pretty much identical things in Serbia and its province Kosovo. And Russia's approach has arguably been more elegant, smooth, and peaceful. Also, the Ossetians and the Abkhazians are more justified to demand their own territory because they are authentic unique nations that have lived at those territories for centuries while "Kosovars" are just a fake nation, a redundant copy of the Albanian nation that was allowed (and, indeed, encouraged) to propagate and reproduce (by Mussolini, among others) more than what would have been appropriate. Legally, the three cases are virtually isomorphic.

When the violations of consistency are driven by someone's own personal interests or his image, the particular case of inconsistency is known as "hypocrisy".

Unfortunately, there are gigatons of it in the contemporary Western societies.

And that's the memo.

Internet Explorer 8 beta 2

Download (EN, DE, JP, simplified CN)
Install instructions (mostly not needed)
IE 8 web page (microsoft.com/ie8)
Release notes (KB 949787)
IE blog, tour (new features)

The new browser can now

• re-open closed tabs (when you open a new tab)
  
• switch to po/rn mode ("InPrivate" browsing: history is not saved)
• autocomplete URLs not only in your history
• autocomplete URLs with thumbnails offered
• increase your security and performance from IE7
• use accelerators (replacing frequent copy/paste between pages)
• use web slices (detailed bookmarks from the toolbar)
• see suggested sites (if you want)
• search on page from a naturally incorporated box
• fix the DPI bug of IE8 beta 1 (incompatibility with a non-standard default system font size)
  
• fix the Operation aborted bug of IE7

Hat tip: Ramanan

GLAST renamed for Fermi: first results

Audio (since 2 p.m. EDT = 8 p.m. Prague Summer Time; RealPlayer needed)
A web page of the press conference
GLAST home page
GLAST prelude (MP3; explanation here)

Just two months or so after GLAST was launched, we will be told about the first results. They will also announce the new name of GLAST: it's Fermi.

The first result is that the gadget seems to be working very well and the luminosity is amazingly promising. Give us ten years, they say. There's a message for all Horgans, Woits, Smolins, and similar stuff from Dawkins: science is interesting and if you don't agree, continue with this video (context). ;-)

Via Tommaso Dorigo.

Glashow: blind chance or intelligent design

Playlist (3/17, an hour in total)

Glashow talks about the crucial interplay between unexpected discoveries and planned research in science. He demonstrates the point on many historical examples. Serendipity means to look for a needle in a haystack but to find the farmer's daughter instead. ;-)

The parts 1/17 and 2/17 are a bureaucratic self-promotion of Honeywell and China but you can see them, too. ;-) At the end, there are some questions. For example, a girl asks Glashow why he switched from literature. It turns out that her assumption followed from a degree Glashow earned, "Bachelor of Arts". :-)

Russia recognizes independence of Abkhazia and South Ossetia

The upper house of the Russian Parliament (Council of Federation) has voted unanimously (130-0) to ask President Medvedev to recognize Abkhazia and South Ossetia as independent countries. By the rules of statistics, it could have been expected that the lower house (Duma) would do the same thing soon: it voted unanimously (447-0) a few hours later.



Medvedev will have to think twice. The recognition of their independence would mean a change of their policy: they opposed the independence of Kosovo. But because the world, including Russia, is slowly accepting that Kosovo has become an independent country, the situation has changed.

Update: Medvedev recognized the countries on Tuesday (video: speech)

I would find it natural (and more stable) for Russia to recognize the independence, organize a speedy referendum, and attach those provinces to the Russian Federation. At least that's what I would be doing as the boss of the Kremlin. A re-unification is particularly natural for Ossetia.

As everyone who understands politics a bit has always known, the Kosovo independence has sparked a natural avalanche of declarations of independence. Czech president Václav Klaus emphasized the role of Kosovo as a precedent from the very beginning. Russia Today has predicted South Ossetia and Abkhazia as the first places to follow Kosovo's example as early as February.

In this now-natural process, I would expect Nagorno-Karabakh to be the next de facto independent country that might be recognized, because of their geographic proximity to the current main epicenter of events. Azerbaijan is already talking about it: its officials are now scared like hell. I believe that the independence of Nagorno-Karabakh - or its unification with Armenia - is a good thing for Moscow because Armenia is friendlier to Russia than Azerbaijan and they might want to recognize their separation from Azerbaijan, too. (The topology of Armenia is already nontrivial.)

Crimea (now in Ukraine) could follow: there are historical reasons to understand why it should belong to Russia and the status of Sevastopol may turn out to be ambiguous even from the current legal viewpoint. Transnistria is a de facto independent, pro-Russian strip that belongs to Moldova de iure and Moscow may want to bring it closer, too: the Russians are already intensifying diplomatic turbulence in Transnistria.



It is unlikely that too many other countries would join Russia in accepting the independence of Abkhazia and/or South Ossetia. On the other hand, I find this question pretty much inconsequential because Russia is who ultimately enforces the status quo in the region, much like NATO is doing the same thing on the territory of Yugoslavia.

NATO and Russia

At this moment, I would consider pure idiocy if NATO were trying to rearm Saakashvili because this guy will obviously lose any hypothetical future conflict with Russia, with a possible (but not guaranteed) exception of a full-scale world war. By his adventures, Saakashvili has already wasted USD 2 billion in the conflict (more than 1 month of his country's GDP) but only a very stupid person could repeat a similar mistake again. (Russia has adopted the usual American nuclear doctrine, the right for preemptive nuclear strikes, half a year ago, and the fear of nuclear weapons has dropped dramatically since the 1980s, so we should better be careful.)

NATO should stop provoking Russia in this obvious fashion and accept that Georgia continues to be a Russian backyard, a status it has enjoyed for centuries, much like e.g. South America is the U.S. backyard closed from the European powers, according to the 1823 Monroe doctrine. NATO needs Russia for many projects, including logistics for the war in Afghanistan. Cutting links with Russia could mean a defeat in Afghanistan, among many other things; Russia wouldn't care, it's ready to break all the ties. Meanwhile, Iran can do whatever it can because people are looking elsewhere. Moreover, Russia is being pushed closer to Iran which is bad.

In the U.S., it is apparently an example of bipartisan political correctness to be against Russia, and to assume that the U.S. can do anything in the Russian sphere of influence. This silly consensus is, of course, primarily created by the manipulative, dishonest media, and hundreds of millions of stupid people who uncritically believe what they read. They may be shocked by reality. And indeed, they should be. ;-)

Richard Dawkins & Steven Weinberg on religion and science

Playlist (8 parts, 85 minutes)

These two prominent atheists, of course, share a lot of opinions. But you can see some funny differences: for example, Dawkins thinks that the anthropic explanations are "elegant".

Joe Biden and global warming

Barack Obama will pick Joe Biden as his running mate. When it comes to climate change, Biden seems to be just another mad man:

Face global warming or global conflict (2-page interview)

As a presidential candidate, he said that global warming will destroy the U.S. military. He is the "best one" to solve the "energy crisis" and wants to reduce CO2 emissions by 80% by 2050 while raising the mandatory percentage of alternative energies to 20%, among many other mad things.

Strings 2008: Friday

You may go to the main Strings 2008 page on this blog; that page includes the live webcast.

This Friday report includes a shortened version of Hiroši Ooguri's summary of all talks and David Gross' philosophical remarks and visions for the future. See also Jester's highlights at Resonaances.

Boris Pioline begins the Friday morning session with a review talk about BPS black holes from the topological string perspective; see e.g. Ooguri-Strominger-Vafa: his PDF here.

Microscopic explanation of black hole entropy is a hallmark test of every theory of quantum gravity and string theory succeeded marvelously. We were slowly going from large-charge BPS black holes to non-BPS and small black holes. He wants to cover OSV; multi-centered walls; MSW; Donaldson-Thomas invariants; improved OSV; 4D black holes and 3D instantons.

Boris reviews some basic type IIA setup in OSV, like in my article about it. He links the F-terms in the effective action with the (A-model) topological amplitudes, including terms with Gromov-Witten coefficients. Boris mentioned the M-theory lift to 5 dimensions. He explains the p,q,J charges and defines a second helicity supertrace, an index with J^2 in it (to swallow the fermionic zero modes), that is almost constant but jumps on lines of marginal stability.

Boris sketches some papers of him with Andy Neitzke and others: unfortunately too fast to catch something useful here. He instantly goes to attractor flows. If Z=0, a solution with a naked singularity should be dismissed. Maybe, a spherically asymmetric shape may become relevant here. The entropy when higher-derivative terms are relevant is given by Wald's formula; the entropy is the Legendre transform of the partition sum. He writes "topological free energy" and says that it was thus natural to write the OSV relation with the Laplace transform.

Questions: are both sides of the OSV well-defined, is it true everywhere, what do the holomorphic anomalies do, is it consistent with elmg. dualities, consistent nonperturbatively? Or, as Cumrun cares, does the formula lead us to a new interpretation of quantum mechanics? ;-)

Boris defines multi-centered solutions; see also attractor flow trees (Denef; Denef, Moore). They carry angular momentum. Infinite proper distances appear in various limits etc. Split attractor conjecture links the multi-centered solutions to the trees and there is a finite number of them. At lines of marginal stability, one loses BPS states. The jump of Omega is proportional to a product of two Omegas. Kontsevich and a collaborator generalized this formula profoundly; see later.

The MSW (Maldacena Strominger Witten) (0,4) SCFT is useful if the D6-brane charge vanishes. It comes from M5-brane on a 4-cycle, with a left-moving momentum. It is a kind of sigma-model. Cardy's formula applied to MSW reproduces the entropy, including the R^2 Wald correction. Some features must be avoided at this simple level, e.g. self-intersections.

To go to higher orders, consider the (0,4) elliptic genus (generalized index). It has to be a combination of theta functions, weighted by some modular forms H. The modular forms may be reproduced by SL(2,Z)-symmetrizing of its polar terms - see fairy tail. The polar terms come from states with dimensions between 0 and a multiple of central charge. The polar states may be described (Strominger Gaiotto Yin) by Landau levels near the poles of S2 (times AdS3). Another approach uses 2-centered solutions.

Bound states of D6 with D2,D0 in a ("very noncommutative") limit are described by ideal sheaves that are counted by Donaldson-Thomas (DT) invariants (related to GW invariants) and MacMahon's function appears here, too. The DT partition sum is written as a scary infinite product with two such factors; the first factor are "halos" while the second are "core states" (a bank I had in New Jersey, before it was bought by First Union and then by Wachowia). ;-)

Take this infinite product, it's a simple calculation, and up to genus 51 haha it can be shown that Omega grows like exp(lambda^3), confirming the 5D BH entropy. ;-) Extreme polar state conjecture says that only 1 D6 and 1 D6bar are needed. I missed the "swing states" but they may decide about Obama and McCain.

Some details are added to OSV now: D6 brane charge must be zero, t must go to i.infinity, DT partition sum must be cut off, a measure factor is added, exponentially small correction are estimated. The "entropy enigma" suggests that OSV can only work at stronger coupling, because of the dominance of multi-centered solutions.

In the last 10 minutes, he wants to use 3D instantóňs (the accents are supposed to be French here haha). He wants to replace Omega by something continuous at the lines of marginal stability, by some patchwork. His moduli space mimics the hypermultiplet but at finite radius, it receives some instanton corrections. Some hyperKähler cone comments are too tough for a blog, if not for me. ;-) But he has a compact way to encode a hyperKähler geometry. Conformal compensators appear, too. Finally he gets to Kontsevich and Soibelman - so you shouldn't be shocked that the lecture was heavily mathematical even a few minutes ago. ;-)

To conclude, a lot of progress in N=2 BPS black holes but not a complete progress. The instantons are promising. O,S,V are congratulated for a prize for the OSV conjecture. Good talk. Unfortunately, Boris didn't hire anyone to ask a question, so there was none. Everyone can join Kontsevich and Soibelman now.

Ashoke Sen also discusses extremal black hole microstates - in a particular context of the AdS2/CFT1 correspondence: PDF here. The talk is based on two co-his 2008 papers, with a few earlier papers as background. Ashoke explains the entropy in terms of microstates and the area. To go to smaller black holes, he needs to learn how to deal with the higher-derivative corrections on the gravity side and with more accurate statistical methods on the microstate side.

The Mac presentation software collapsed for a while but it's back now.

The microstate side is well understood (see Boris above) so he will focus on the higher-derivative (Wald-like) issues on the macroscopic side. For BPS black holes, Wald's formula simplifies to "entropy function formalism". It starts with a partially proven proposition that extremal black holes have an SO(2,1) symmetry - i.e. an AdS_2 factor - near the horizon. The remaining dimensions are compact and fibered over AdS_2.

From string theory on this near-product space, he focuses on gravity and U(1) fields, and writes their configuration (metric plus gauge field) that preserves the SO(2,1) symmetry, determined up to a scaling of metric and the field strength. He defines "script E", by a transform of the Lagrangian (2.pi times (e.q - v.L)). Near-horizon quantities are obtained by extremizing E with respect to v,epsilon. And the value of E at the extremum is the entropy itself!

He will now try to generalize this formalism by adding higher-derivative corrections properly. SUSY won't be explicitly used. Semiclassically, his treatment will resemble the Euclidean black hole reasoning. He will assume no multi-centered states spoil his single-centered calculation - he can assure it by setting the attractor values at infinity, too. Ashoke writes the Wald entropy draft "Z in AdS_2" as an OSV-like Laplace transform of d(micro). The entropy is the log of d(micro) and the rules are supposed to coincide with the AdS/CFT expectations.

The SO(2,1)-invariant solution is Euclidean-continued. The gauge field must vanish at some complex positions. To check his formalism, he wants to reproduce Wald's formula. The partition function Z goes like exp(-A) where A is the Euclidean action. The latter needs an IR cutoff of "r" to avoid a divergence.

In "A", the boundary part is linear in "r0", no absolute piece. He keeps the nice, r0-independent part of "A"; imagine that the cutoff-dependent one is removed by a boundary counterterm. So he gets a rather simple proposal. The exponential of -2.pi.v.Lag_2(e) equals the sum of d(micro) multiplied by exp(-2.pi.e.q). Wald's entropy is then equal to ln(d(micro)).

So far he worked with AdS2 and the Z partition sum was properly called this way. To see why CFT1 matters, he first renames it to Z(CFT1). ;-) He changes the convention for UV/IR cutoffs, making all scales "r0" times longer than usual (only the ratios matter). Frankly speaking, I completely missed how he used anything about CFT1 in the following discussion: it really looks like he only renamed things to "CFT1" but that's probably because I didn't listen as carefully as needed.

Some simple measure factors should be calculated now, including quantum corrections. I thought that none of them should be there according to Andy et al. To summarize, he proposed an OSV-like formula for extremal black hole entropy, claiming that it has an AdS2/CFT1 spirit. Cumrun was too far so I didn't hear his questions too well but Ashoke says that there can be various boundary terms. Hiroši continues with a similar question about finite-size effects. Ashoke says that these come from the AdS interior, making his favorite term unambiguous in the limit. Shiraz raises a conjecture. It's confirmed: the Hamiltonian has a discrete spectrum, and they found something by looking at limits of the BTZ black hole.

Strings 2009 will be in Rome. Some more workshops such as New Perspectives in String Theory are announced.

After the coffee break, Greg Moore talks about developments in BPS wall-crossing - his work with Gaiotto and Neitzke (Davide is on a karate-picture, claimed to struggle with a paradox). After Greg reviews wall crossing, he will talk on the Kontsevich-Soibelman-related stuff. That will be hard. Kontsevich and Soibelman showed that Greg's related 2007 talk about wall crossing in Madrid was far from complete.

He begins with an N=2 theory with a moduli space and symplectic lattice of elmg. charges. He recalls Boris' second helicity supertrace Omega, talks about walls of marginal stability and BPS bound states of other BPS states. For example, an orange, a lemon, and an egg form a bound state that looks like an orange but it has a lemon inside and an egg inside it (with a bird). ;-) Denef-Moore's formula for the jump of the index only applies when at least one decay product has an elementary electric charge.

The Kontsevich et al. formula is meant to generalize it to a pair of non-elementary charges in the lattice. A picture of BPS rays is "as close as we get to the LHC in this talk". ;-) Instead, a product over all symplectomorphisms over a whole set of rays may hint that it would be a good idea to give up the detailed content. ;-) At any rate, a product compensates changes of the jump in the index, to remain constant across the wall.

Seiberg-Witten theory is formulated as lattices fibered over the u-plane, with monodromies. He adds toroidal fibers to write the effective action. The G=SU(2) case is shown explicitly, with the two monopole and dyon singularities in the u-plane. At this moment, I am confused about a basic point - where he lost gravity (at the beginning, we were thinking about black holes, didn't we?).

Greg wakes up the audience because he wants to explain the structure of a space. The quantum corrections depend on the BPS spectrum. The wall crossing formula - the Kontsevich et al. formula - now can be derived from the continuity of the metric across the wall. The metric is continuous but it is not a trivial constraint because of the dependence of the quantum corrections in it on the spectrum.

To actually show this derivation, he considers a twistor space. Fibers appear in almost every sentence and almost all letters in the formulae are Greek or script-letters or they have at least heavy math-cultural accents such as asterisks. ;-) Why I am bothering you with all this? Because someone has a canonical symplectic form! Semiflat holomorphic Fourier modes, whatever they exactly are, help him.

On a point in the moduli space, he chooses a basis to reorganize a calculation as a weakly-coupled one. At one-loop level, he's led to a periodic Taub-NUT space, with some Bessel function in it. Suddenly a differential equation for some twistor modes enters the scene.

Chi_inst, one of the two factors in chi, is proportional to the exponential of an integral with some poles in it (two months of probing every possible mistake). As a function of zeta, Chi is therefore discontinuous across the wall.

He wants to go beyond one loop (to see all BPS states) but effective field theory is not usable here. Instead, they solve a Riemann-Hilbert (RH) problem. Instantons are written explicitly as a sum over trees. Again, KS WCF comes from continuity of the metric. How do they check that their hyperKähler metric is physically the right one? The RH problem is equivalent to some differential equations - and they physically correspond to R-symmetry, scale symmetry, holomorphy.

In Stokes' phenomena here, factors are u,R-independent. End of proof, summary: they constructed HK metric for Seiberg-Witten on circle and other things said above. The work is related to various work of Ceccotti, Kapustin, Hitchin, and others. In future, singularities at superconformal points should be studied, besides integrability on motivic version of WCF. Finally, generalization to SUGRA (that's what I thought was necessary but it was not). What is the relation to work of Joyce and others? Compute some moduli spaces etc. Thank you.

Cumrun asks whether the continuity is related to the continuity of something else in an infinite-dimensional case of Cumrun, and Greg gives a mixed answer. Someone said that duality in 2D will prevent him from generalizations. Cumrun says a few more things I can't hear well but Greg talks about many isomonodromic deformations that can arise. The last question is about the extension from regions in the u-plane to compact manifolds etc.

Davide Gaiotto contributes a talk about his recent 3-paper work with Edward Witten about S-duality and boundary conditions in N=4 SYM; he's written many other recent cool papers, too: see his PDF here.

There are many boundary conditions - jungle - even if you impose symmetry constraints. He motivates the work by everything about N=4 being interesting, and by a generalization of Wilson lines and surface operators to the co-dimension one case, as well as by the Geometric Langlands program in maths.

Davide reviews the symmetries and parameters of N=4 SYM and its 10D SYM possible origin. Boundary conditions break some translational and therefore super- symmetries, too. OSp(4|4,R) is the maximum preserved supergroup of PSU(4|2,2). For example, Neumann boundary conditions set F_{3i} to zero, much like some components of scalars and derivatives of others; a gauge symmetry survives at the boundary.

I wonder whether it would be more natural to study these things as orientifold planes rather than strict boundaries.

The generalized Neumann conditions allow some fields to diverge (as 1/r) while d_3(X) can be related to epsilon [X,X]. New boundary conditions may be obtained by S-dualizing the known ones. Moduli spaces will probably be found and nontrivial theories may live inside the boundaries.

He obtains new complex boundary conditions as "bound states" of known domain walls and simpler boundary conditions (or flowing their parallel arrangement into the IR, as he says). Some braneworld realization with D3, D5, NS5 intersecting in various directions follow. D5-branes add 3-5 strings while NS5-branes split D3-branes and create new 3-3 strings.

Among other simple example, he claims that Neumann and Dirichlet boundary conditions are S-dual to each other (electromagnetic duality). When charge 1 hypermultiplet is added to the Neumann ones, one obtains S-self-dual conditions, as can be seen from a Hanany-Witten stringy construction of the setup. The result is nontrivial in field theory, analogous to particle-vortex dualities in 3D.

Neumann with several charge 1 hypermultiplets is dual to Neumann coupled to a strongly coupled 3D theory on the boundary. Quiver picture of it is here. More importantly, they seem to have a prescription to construct S-duals of the boundary conditions. SL(2,Z) is generated by S,T. T adds a Chern-Simons coupling at the boundary and they can check that (ST)^3=1 and S^2=1.

He may view their procedures as a tool to engineer new 3D theories (on the boundary) and find new mirror pairings between them. The holographic dual of the boundary conditions should be found, he says, and people may try to generalize the conditions to lower SUSY. Hiroši asks a question but I cannot extract any useful information from the answer, sorry. Cumrun asks what happens for various gauge groups, especially the exceptional ones. Somewhat surprisingly, no interesting answer.

Now I am looking at mail. Andrei Starinets wrote an amusing correction to my Thursday text (I have roughly 100+ visitors a day from cern.ch these days haha). He confirms that what he cares about is the ALICE detector, as he correctly said, of course. But he incorrectly used a picture of the ATLAS detector, and someone correctly told him about the mistake. ;-) He doesn't like when their AdS/CFT treatment of heavy ion physics is referred to as a part of AdS/QCD. Sorry, but I will probably keep my imprecise vocabulary.

Simeon Hellerman ends the morning session by cosmological unification of string theories - his work also including Ian Swanson about the interpolation between string theories of very different kinds (e.g. super and bosonic or supercritical ones): PDF here.

Simeon began with the hexagon duality network for M-theory and says that when SUSY is broken, we don't know much but we know his papers. ;-) As I explained in several blog articles about these issues, Ian and Simeon work in the light cone gauge, adding nice profiles of tachyon and dilaton that lead to fully conformal theories.

The theory in their picture is typically conformal for a simple reason - all the Feynman vertices are "outgoing" so you can't even construct loops such as those for the beta-function. Their first interesting cosmology looks like a bubble of nothing - an expanding hell with a tachyon vev that expels all strings.

Now, he allows the tachyon to (quadratically) depend on a transverse dimension X2, too. The coefficient grows with time. X2 is massive and physically disappears. All X2-excited modes are killed in the bulk of the bubble. It looks like he is reducing the critical central charge. Well, now the theory does have 1-loop diagrams, but not higher. I had to look outside now, but I guess that he explained that the central charge is transmitted to a linear dilaton?

Now, he looks at the interpolation between type 0 and type II. The interpolation allows you to say that SUSY is spontaneously, not explicitly broken in type 0. Finally, Simeon interpolates type 0 and bosonic string theory, extending an old Berkovits-Vafa construction to the level of a full cosmological solution. In the context of E8 heterotic strings, he wants to follow the fate of the gravitons, use the insights of Hořava and Fabinger, and other things: they construct a new non-SUSY E8 string and he presents its spectrum.

His next goal is to connect the N=2 superstring (with the D=4 real critical dimension). To conclude, his "big picture" connecting the theories looks like complicated ladders - box diagrams - showing the transitions of supercritical strings to other strings etc. Time-dependence is essential to connect them and many other links may be waiting to be discovered. A very good talk.

A question asks about some UV/IR links, the tachyon storing the information about the high-dimension spectrum etc. The answer is a bit ambiguous but Simeon proposes a precedent. Simeon is sad that no one asked about phenomenology because he would show that their preliminary graphs are promising (the graph was not shown to the camera, too bad). ;-)

In the afternoon, Johannes Walcher talks about the tadpole cancellation in topological string theory; see his paper. To start, topological strings are both toy models for string theory as well as a tool to study BPS-protected stringy quantities (F-terms). He will look at top. strings on compact Calabi-Yaus with both D-branes and orientifolds.

In type I physical string theory, anomaly cancellation is one of the things that initiated the 1984 revolution. On the worldsheet, it comes from a cancellation between boundaries and crosscaps: tadpole cancellation (vanishing of the 1-point function of the RR 0-form). Now, yes, topological strings also exhibit tadpole cancellation: A-model and B-model can only be decoupled from one another if the total charge is canceled between the D-branes and orientifolds. Otherwise, the loop amplitudes would suck. SUGRA/spacetime interpretation is not yet known.

Open/closed topological string theories for noncompact, local manifolds were solved in this century by Vafa and various collaborators (with Dijkgraaf: via matrix model; with Aganagič and others: using the topological vertex). To define topological strings, he twists - interprets various supercharges "G" of the physical string as BRST operators "Q" and/or antighosts "b". Mirror symmetry exchanges the A- and B-models. He also introduces anti-A and anti-B models, CPT duals of A and B. They're probably equivalent to A,B and the role of the new concepts is not quite clear to me now.

BCOV 1993 shows that B-model amplitudes depend on CS moduli nonholomorphically: that's the holomorphic anomaly, arising from the boundary of the Riemann surface moduli space. BCOV showed that closed string amplitudes don't depend on the "wrong" moduli.

Witten 1993 included D-branes to topological strings: A-branes are Lagrangian submanifolds with flat bundle; B-branes are holomorphic branes with holomorphic bundles. The corresponding charge is carried by the "other" model: Ooguri-Oz-Yin 1996 (no, it's not Xi Yin who was in the kindergarten in 96 and was only starting with the A-model).

Back to the tadpole cancellation. He must extend the holomorphic anomaly equation first. The integration constants must be determined. For the quintic, it's computed up to genus 51. So the normal BCOV holomorphic anomaly - one for closed strings - must be extended to the open string. The moduli space talks about Riemann surfaces with boundaries, so it has new (codimension one) boundaries itself.

By now, we've included D-branes but orientifolds are needed to cancel the tadpoles. Strings themselves become unoriented. Klein surfaces have genus g, h boundaries, c crosscaps. 2 crosscaps can be traded for 1 handle (as far as at least 1 crosscap is left), with chi=2-2g-n-c. He says he doesn't know a textbook saying that, and I am convinced that even Polchinski does. These surfaces may also be viewed as Z2 quotients of closed oriented manifolds.

He's summing the amplitude over the number of crosscaps 0,1,2. The sum obeys the extended holomorphic anomaly equation. Now he jumps to some old stuff - Gopakumar-Vafa 1998 interpretation of the topological amplitudes as BPS state counting. RHS = sum of powers of sinh. Open/unoriented amplitudes of this kind go back to Ooguri-Vafa 2000 (and Walcher 2007). The expansion coefficients are integers iff you cancel the tadpoles between orientifolds and crosscaps (not an obvious relationship). It's natural for him to say what real top. amplitudes are counting - well, real enumerative invariants (Welschinger, Solomon etc.).

There are two ways to embed an A-model setup to type IIA, one with O6 and the other with O4. I didn't quite get this: they seem to be geometrically different, even in the 6 compact dimensions, don't they? For the O4/D4 he gets a better picture, with the topological tadpole cancellation linked to a local cancellation in the physical string.

Speculations: Witten interpreted the hol. anomaly as evidence of background independence of the top. string. The translation of the anomaly in terms of infinitesimal Bogolyubov transformation is given. As Cumrun Vafa likes to say, the partition sum is not a function, it's a "wave function".

Some Psi doesn't coincide with the closed Psi; why should it? There was the first speculation 1 here, not sure what it exactly was. The speculation 2 says that top. string is only OK if it is possible to effectively reduce the number of relevant states to a finite number. No questions.

Marcos Mariňo is going to remodel the topological string, both perturbatively and nonperturbatively. He has a black T-shirt but I can't say whether it is Che Guevara on it or another comrade. Optimistically, it looks like a revolutionary after counter-revolution. The work is based on work with Bouchard, Klemm, Pasquetti, and others (previous work).

Marcos believes that topological strings are less complex than superstrings but more complex than noncritical strings (the latter is not clear to me). A goal is to compute everything, at once if you can - which you can with the matrix models. Mirror symmetry together with the B-model is helpful, too. Pichard-Fuchs equations encode what you need.

The holomorphic anomaly etc. can be used to solve the equations recursively but the boundary conditions are unknown and make it complicated, except for cases when they're known, e.g. gap conditions of Huang and Klemm.

Marcos is reviewing the Dijkgraaf-Vafa 2002 solution of the B-model. On a particular geometry, the partition sum is obtained from a large-N matrix model with a potential related to the functions that determine the shape of the local Calabi-Yau. Unfortunately, these B-backgrounds have no A-mirrors.

He wants more general manifolds, e.g. toric manifolds. They have fun moduli spaces, rich enumerative content, large N (CS-like) duals, mirrors in terms of algebraic curves. They're helpful for N=2 engineering. A toric picture (triangle with 3 external legs) and its thickening is explained. They can be also encoded in toric A-branes with some open moduli.

How would you remodel the B-model on the background? I would first like to know Why I would be remodelling it. Did someone mismodel it? ;-) I might misunderstand what he means by remodelling. Under the remodelling title, he writes some schematical recursive formulae - a complicated closed surface equals another surface with one thin bridge plus two surfaces connected by a thin bridge. These amplitudes solve the loop equations and give a 1/N expansion of the matrix model.

A conjecture wants to compute B-model TS amplitudes from the mirror curve - residue amplitudes on it - in a format resembling matrix models. The Dijkgraaf-Vafa backgrounds obey it automatically but even if you don't have an explicit matrix model, you can calculate. Motivation comes from string field theory of the B-model (Kodaira-Spencer theory) for the noncompact case. He gets a general theorem for all toric CYs but what the theorem exactly is is not too clear. But it's probably the picture formula for the amplitude written in the middle. It follows that these amplitudes obey loop equations. An application to a local P^2 is shown. A test against some explicit orbifold calculations works. Another test passes: a comparison with Wilson loop vevs in a dual large N Chern-Simons theory (on a Z_p orbifold of S^3), for local F_p. With a nontrivial modular transformation, one can interpolate weak and strong 't Hooft coupling regimes.

In the last 5 minutes, he talks about non-perturbative physics of topological strings. In the matrix models, non-perturbative effects include tunneling of eigenvalues. However, these terms are contour-dependent, implying a non-perturbative ambiguity (theta-angle-like). In the double scaling limit, they become spacetime instantons due to ZZ branes.

As usual, these instantons control the large-genus behavior of the perturbative series. One can derive something about the singularities in the Borel plane. One large-order test worked out well. These instanton effects become domain wall in the full physical string. He is running overtime now. Oh, I see: Z_{MM} is matrix model. I thought it was Marcos Mariňo.

Nontrivial tests convince you that the holographic dual is really the CS theory on the lens space. He wants to get a background independent topological partition sum by summing over all non-perturbative effects, a statement whose precise meaning is unfortunately not transparent to me.

OK, so they generalized the matrix model calculational framework, which also generalized special geometry to higher genus that avoids holomorphic ambiguities. Also, there should exist a "special" brane analogous to the ZZ brane in 2D gravity. Thank you very much.

Someone asked what happened with an old well-known non-perturbative ambiguity of matrix models. Marcos says that it's fixed in one model but not sure about other models. Cumrun Vafa asks his first question about the existence of matrix models and/or matrix integrals in some cases. Marcos can write the integral but sees no reason why the matrix model should be the correct one. Cumrun's second question is surprise that the result is always a sum over saddle points. Marcos says that it is universal for his backgrounds. Applause again.

Before Hiroši Ooguri summarizes the conference, the list of organizers is read. Applause of grateful participants follows. Younger generation was more exposed and great things are going to happen. They're going to live under pressure - seeing experimental discoveries for the first time in their life.

Hiroši thanks again. It's his 2nd summary, after 2004. Four years ago, Gross told Hiroši there are two ways to give the summary: summary talk or vision talk. The first one requires him to attend all the talks and he already did it in 2004. So the other method is the vision talk, which is why he will give the traditional summary talk.

(1) String theory is a candidate - a picture of Obama and McCain. It should govern everything - a childish picture of galaxies and everything.

(2) String theory is also a model (I thought an attractive woman would appear here, not...). It is already a good approximation of the real world and explains new things - for example how the Hawking's seemingly robust argument for information loss could have gone wrong.

(3) String theory is also a tool to study many things.

(4) String theory is a language, giving us new concepts (instead of normal geometry etc.) for the Planck regime etc. E.g. Freddie showed that one doesn't need Lagrangians (even though it was not exactly the most stringy talk).

Among the 1,2,3,4 values, important work often plays several roles. But he has to divide the talks into the four categories arbitrarily, anyway.

In (1), he talks about string phenomenology. Realistic models may be rare and predictive. Ibáňez reviewed the MSSM landscape, Weigand included orientifolds, Donagi looked at the High Country - one best model they have, Vafa offered his bottom-up, comparably unique F-theory alternative. He has to ask: is there any problem left or should they be all fired? Shih solves general gauge mediation and Verlinde looks at mediation holographically. Kallosh reviewed future cosmological tests of stringy models. There is already tension: chaotic inflation is hard.

In (2), Hiroši mostly means - even though doesn't explicitly say - generic features of quantum gravity, as seen in string theory. Veneziano studies high-energy scattering, including trapped surfaces. It could be useful to see something about information non-loss. Strominger talked about the chiral 3D gravity, possibly relevant for 4D extremal Kerr black holes.

Hiroši summarized Polyakov's talk better than I understood it: particle production screens cosmological constant in de Sitter space much like Schwinger effect screens magnetic field. Hellerman presented cool things about time dependence, decays into nothing and completely different types of string theory (bosonic, supercritical, non-supersymmetric). Simeon is employed by IPM, a Japan-funded institute meant to take over the Universe. Murayama is the boss and Susanne Reffert's picture is also shown to make the slide smarter and prettier. They have up to USD 200 million for a decade.

In (3), it's a tool. Here we talk about applied string theory. Gubser and Starinets talked about quark-gluon plasma, Hiroši says. The transport coefficients are now calculated, heavy quarks are calculated, with nicely working links to RHIC, LHC, lattice QCD, and others. Hiroši asks how to quantify theoretical errors. Minwalla showed the equivalence between Einstein and generalized Navier-Stokes equations from hydrodynamics. Starinets proposed a new strongly correlated liquid with a bulk dual.

In (4), strings are a language. Hiroši believes that the S-matrix theory is returning. Schwinger is quoted as saying that the complex plane is the top discovery of particle physics. It may be the twistor plane. Dixon found some new structures in the helicity formalism. Berkovits explained fermionic T-duality. Sokatchev showed it works for a weak 't Hooft coupling while Alday did the same thing, using AdS/CFT, at the strong coupling. In both limits, one can see the exponentiation.

String theory and QFT (boy and girl) are making progress hand in hand and we may see the full answers soon.

Cachazo showed a remarkable convergence of N=8 SUGRA at large complex momentum. The S-matrix is determined by the leading singularities. The Lagrangian becomes unnecessary for the S-matrix: a yet new language to formulate quantum field theory. Green showed how dualities and string theory expansions constraint the amplitudes in SUGRA. In Hiroši's opinion, the finiteness of N=8 SUGRA is an open question. Stieberger showed remarkable simplifications coming from SUSY Ward identities.

Steps have been made to prove the AdS/CFT correspondence. The planar Yang-Mills should be reproduced from the worldsheet. Integrability has been helpful for these things, to check the anomalous dimensions of operators etc. Staudacher considered a more general limit L/log(M) is fixed, where L is the number of derivatives and M is a number of letters.

There has been a discrepancy between AdS and CFT at four loops and Hiroši is surprised that no blogger has used it to "disprove AdS/CFT". I think that Hiroši heavily overestimates numerous capitalist imperialist pigs and Woits, among similar dense stuff. (By Woits, I primarily mean a chap called Mr Lee Smolin who dedicates a nearly whole chapter of his dumb book to speculations that AdS/CFT is invalid, but if you want to see that Mr Peter Woit also considers AdS/CFT "damn conjectural" and even ill-defined, see here.) They couldn't find what's going on at the four-loop level! Maybe if the paper was called "String theory sucks and unravels at four loop level". ;-) I've known about the discrepancy but it was always clear to me that it's due to a subtle term neglected in the spin chains because the spin chains were simply not quite identical to the exact theory. Janik removed the discrepancy, anyway.

Hiroši talks about the membrane minirevolution, a possible new kind of Chern-Simons-like theories that could have analogous to N=4 SYM from many viewpoints. Lambert reviewed the maximally supersymmetric theory, Maldacena reviewed the N=6 theory. Now Hirosi switched to the squashed sphere and included Tomasiello's talk about the CP3 AdS stuff.

Pioline reviewed the OSV conjectures from the microscopic viewpoint - the more abstract mathematical one - and Sen was adding derivatives in the macroscopic, black hole description. Mariňo essentially gave the mirrors of toric manifolds, derivable from Kodaira-Spencer theory, and a method to calculate non-perturbative effects (summing over branes, in the top. case: sum over Calabi-Yau geometry). Hiroši thinks it's quite radical and should be compared with existing knowledge about OSV.

Moore discussed how the counting jumps on the walls, giving a nice derivation of the Kontsevich-Soibelman formula. Gaiotto discussed how S-duality maps a large class of 1/2 BPS boundary conditions. String theory is an extreme sport and he enjoys to look at the parade of beautiful ideas. Hiroši shows Gross' transparency in 1998, right after AdS/CFT began. Hiroši wonders whether he forgot a talk. Let's see. He says: AdS/CFT has a huge range of validity and he wonders whether there's place for loop quantum gravity in it.

Sorry, Carlo, but Hiroši did forget, after all. ;-) Or didn't he?

403 people from 36 countries participated. The numbers are summarized under the Olympic circles. The most active countries have already hosted the conference, which is why they should do it again. Hiroši enumerates a few German, British, and U.S. cities that he would apparently like to visit. ;-) Hiroši thanks local secretaries and other organizers. Applause!

Someone asked how many string theorists there are, comparing with 200 loop quantum gravity magicians. Hiroši has no idea.

David Gross looks in the future and he was the optimal choice for a public talk. He starts by thanking the organizers for a wonderful conference, especially for the great review talks in the morning. Gross won't thank that he was asked to speak.

Gross decided to be completely revolutionary and he won't use any PowerPoint, blackboard etc. (Also because he had no time to prepare them - but he is still a revolutionary!) Someone else was able to speak about planets without any tools: it was a tour de force. Gross says that others like Elias know Gross as the last grandfather who remembers interactions of theory and experiment. ;-)

David recalls that 40 years ago, CERN was a center of theory while the centers of experiments were elsewhere, e.g. SLAC. David wrote one of the first papers to generalize Veneziano's formula. The paper had a contrived name and it was a failure. It's nice to see that CERN and string theory survived for 40 years and are both flourishing. It's amazing and a lot of things have happened.

Both survival stories are fascinating. CERN is pretty much the only lab that survived. Also, only one theoretical umbrella survived in theoretical physics and it has eaten everyone else. So we can see people like string theorist Andrei Linde here, string theorist Lance Dixon, ...

The only discipline that string theory has not yet eaten is loop quantum gravity but Gross is not sure whether we want to! ;-) Needless to say, crackpots are appalled by Gross' comments! :-) String theory will of course never be buried because it already includes the Standard Model and it is a working model of quantum gravity and a unifying theory, much like a tool for nuclear physics, condensed matter physics, mathematics. No one expected that 40 years ago when it was a half-baked theory to describe the nuclear force.

Much like other string meetings, it's been extraordinarily exciting. Unlike other conferences, there have been no great revolutions. There have been a couple of minirevolutions, or as Jeff says, insurrections.

Someone can't understand how they can do experiments with 2,000 collaborators, and Gross is not certain either. But it's because it's not one experiment but one world of experiments. And string theory is kind of similar.

Gross was also excited to see the LHC that will run in two weeks and feed us with new data. When it comes to string theory, the progress in the calculation of gauge-theory quantities is remarkable. They were beautifully reviewed and discussed and the progress both for QFT and string theory was enormous. Gross was really impressed by fermionic T-duality explanation for the dual superconformal symmetry. Ah! It's so obvious when we see it.

Together with the unbelievable advances in integrability of the closed sector of the N=4 theory, we are gaining evidence that the planar limit will be solved. We may be close to it. Janik's calculation of the Konishi operator anomaly is just stunning.

And the membrane BLG-ABJM is just beautiful and will lead to hundreds of papers in the two years. A lot of tools and applications. Progress in string phenomenology is beautiful. It's great to see Cumrun transformed into a phenomenologist - a bottom-up one. ;-)

Things were not discussed here: there was no talk on string field theory and the only anthropic talk was moved after a dinner. So he doesn't have to talk about them and he won't. ;-) But let's ask: what do we really want to learn from the LHC? We will discover SUSY because much like your humble correspondent, Gross has a lot of bets on it, too. ;-) SUSY will be extremely important to learn about but it won't be enough to crack the deep questions or to prove that string theory is right as the "candidate".

We might be lucky to produce black holes (whispering) but it is very unlikely. Nature owes us something - something totally unexpected. Of course, we will abruptly realize that the unexpected thing was an obvious prediction of string theory. Condensed matter physicists found the Hall effect "obvious" once it was seen but even at that time, they were not visionary enough to predict the fractional one.

Gross is going to be critical. String theorists in Hiroši's 1,2,3,4 were following the lamppost strategy. There are thousands of lampposts. They're really lasers, not old-fashioned lampposts, and not enough work is dedicated to connecting the lasers and build new lampposts. Gross was disappointed not to hear about three kinds of things. (Young people, go to the darkness!)

Gross wanted to hear an alternative to the anthropic principle, which we know is wrong, right. (Yes, of course, :-) David!) But to do better, we must explain the cosmological constant differently. Gross wanted to hear more about time dependence, besides Simeon, including string cosmology. Stationary/BPS lampposts are safer and good cosmological lampposts are not available.

Third, what is string theory? Everyone is testing AdS/CFT. Maybe it's time to admit that it's true. There's no value of further tests. No one has any doubt that it is true. When someone says "this is another test", people should ask "what is it good for?" Maybe, can you use the tests to answer What is string theory?

AdS/CFT is the equivalence between two rich, but not impossible, structures. That makes it priceless. We have other, less useful dualities where one side is trivial and the other is hard. For example, there's a duality between perturbative string theory (for 4 decades) which is easy and classically solved (Veneziano) and a theory - Matrix theory - that's impossibly hard to calculate.

If we fully solve the planar limit in a few years, have we solved string theory? No, only classical string theory. If you manage to go to finite N, is it a solution to string theory? Well, if you made it independent of the background and go e.g. to the flat space, by adding higher-dimension operators (moving you away from the horizon). It seems impossible right now to allow the motion in all directions. Non-commutative theories perhaps give us hints of some safe directions where you can move.

This was about the question What is string theory? What fundamental equations govern all of it? These are the future topics he would love to hear. But Gross doesn't want to end up with a pessimistic mood. It's, in fact, fantastic that we have such great questions. The history of the field assures us that it will remain rich and dynamic for many years. And we should be assured to get some hints, and maybe crucial ones, from Nature.

Just amazing thinker and speaker! Flowers for two key ladies among the organizers and thanks to all the speakers (and participants).

Monday, Tuesday, Wednesday, Thursday, Friday

Strings 2008: Thursday

You may go to the main Strings 2008 page on this blog; that page includes the live webcast

Steve Gubser begins the Thursday session with a review talk about AdS/QCD and QCD at finite temperature: his PDF is here.

The first task is to find the free energy of the near-extremal D3-brane, whose metric is written down, at strong 't Hooft coupling. The result is 3/4 of the free result plus a term proportional to zeta(3). A few nuclear physicists joined the research of string theory - or at least they wrote down the Padé interpolation (ratio of polynomials) of the weak-coupling and strong-coupling formulae. (Planck was successful and exact in this business, so why not try again?)

Another slide is about the ratio of shear viscosity and entropy density - recall the 1/4.pi bound that remains the most popular quantity that has been reproduced by experiments. Viscosity is the divergence of "u" in the rest frame, he says, but it is instantly evaluated from a correlator of two copies of the stress-energy tensor. Meyer is very conservative - in Steve's opinion, too conservative.

The elliptic flow is an important phenomenon that can be measured experimentally: the pressure gradient is much larger in one direction than the transverse one (therefore the ellipse). He tries to parameterize it by ideal hydrodynamics but already a small viscosity changes a lot. Professionals can say what eta/s is favored and it agrees with the stringy value, even though some weak-coupling estimates would differ by an order of magnitude. Regimes tested by the RHIC (past) and LHC (future) is shown on a graph.

Steve returns to the theory and allows the bulk stringy AdS Lagrangian to be generalized, to include an arbitrary function. A choice gives very good agreement: not shocking that one function can reproduce another function. At least, he should get something interesting for the viscosity: some messy graphs are shown. If I understand well, this portion of the talk is only interesting for you if you know some recent hypotheses proposed by some heavy ion researchers, about a large viscosity at some transition. Steve thinks it can't work. Well, for me these are two rather messy and contrived pictures and I am agnostic about both, assuming that Steve knows more what he is doing.

The trailing string, another recent work of Steve and others, studies a quark that loses momentum: the loss rate is proportional to the momentum itself. The quark is an animal with a tail/string that probes the AdS bulk. This concept has links with the quark-antiquark static potential that he draws as the function of the distance. In this context, he compares string theory and lattice QCD.

Other graphs show what it means that "charm quarks flow", in the RHIC jargon. Some imperfect yet "respectable" agreement is blamed upon having N=4 instead of QCD: these are the fuzzy standards of QCD (and AdS/QCD). Frankly, I couldn't get too excited by a field where every answer to "does it work?" is so fuzzy.

Jet-splitting is beginning with data about quarks that can get out without interactions after some hard scattering: he shows what gets out as a function of an asimuthal angle. String theory says that the heavy quark is slowed down but he wants to know where the lost energy is going. He shows some flow chart, with a kind of vortex.

From heavy quarks, he gets to light quarks: jet quenching. Some broadening of momentum whose precise nature I didn't understand (transverse momentum squared goes like the distance, and the coefficient is to be calculated) is reproduced rather well by a Wilson line calculation, even though the perturbative answer is off by a factor of 3. Gubser decided to calculate the loss of a gluon's energy by a model with a falling chimney/string. The distance traveled is a 1/3-th power of some energy. He wants to include some response of gravitons etc. - I don't understand why exactly this thing.

At the LHC, one expects an even higher multiplicity from heavy ion collissions, tens of thousands, than at the RHIC. Gold collisions at RHIC make 38,000 particles or so - a number he wants to get from black holes in string theory, from the size of their horizon. So they get the entropy, from the trapped surface, 35,000. But that's clearly pure numerology. He even got some powers incorrectly (1/2 vs 1/3) and the numerical coefficient might be wrong, too. I don't quite know why he talks about this calculation at all.

To conclude, he thinks it's fun, close to experiment, and what makes it hard is that sometimes they're not comparing string theory directly to experiments but only to some prevailing and possibly wrong interpretations of the data. A very technical question: the answer is that reasonable people may sometimes disagree.

Cumrun Vafa asks why the equivalence should work in the first place. Answer: because of some universality in gauge theory. A repeated question from Cumrun is too deep - or vague? - for Gubser. ;-) I would say that Cumrun's complaint is identical to mine - he doesn't have a control over what should work and what shouldn't work. It's about a messy adaptation to random successes. Another question, from Juan Maldacena, is answered by stressing the importance of real-time evolution (over static things). Another question led to an explanation of the quasinormal modes that bring the black hole into the static shape after a time they were calculating.

Matthias Staudacher continues with a related topic, a review talk about the integrability of the AdS5 x S5 AdS/CFT with N=4 SYM on the boundary. The BPS, non-dynamical tests have worked for a long time. Recently, dynamical, non-BPS tests have worked beautifully, too, he claims.

Staudacher promotes these topics as philosophically pleasing, interdisciplinary, and linked to deep maths. A review of gauge theories - and N=4 - follows (the pretties theory). He says that it's not understood where its integrability comes from. There should be a field redefinition where it's manifest (it's clear neither from IIB nor from N=4 SYM). Superconformal groups of the background and IIB backgrounds are briefly explained.

Some words about spin chains. The energy is part of the (superconformal) symmetry here. The spectral problem of N=4 SYM is about the spectrum of operators in the theory and their dimensions. The classical problem (sigma-model) has been fully solved in terms of some curves. Also, the 1-loop dilatation operator has been diagonalized by a mapping it to an (integrable) Bethe Ansatz.

The BMN-like operators are mapped to a chain. At one loop, the interactions are near-neighbor. Long-range interactions arise at higher loops but the S-matrix is believed to factorize. The S-matrix found by people is unitary, obeys Yang-Baxter equation, and the crossing symmetry. He shows some messy all-loop Bethe equations. The system has surprising links to the Hubbard model. A function f(g) is shown to exactly agree in string theory and gauge theory. Staudacher invites people to calculate 3-loop things in string theory and 5-loop tests in gauge theory to improve some tests.

Pictures show hole distributions, not sure what the pictures exactly mean. They're of the type that they can only be understood if you've already seen all these answers. Add some SO(6) sigma-models - a full map between a limit of N=4 SYM and a thermodynamic Bethe Ansatz has been proven to work exactly 2 months ago. The Bethe Ansatz is not perfect: you can only trust it up to L loops where L is roughly the length of the operators (plus one), because of some wrapping problems. There are new ideas how to fix similar bugs.

Sometimes, more answers are known than the questions again. We don't even have the full 2-loop dilatation operator (in all sectors), so what are we diagonalizing, he asks? He wants to know other integrable CFTs, too. A commercial break: he announces regular annual conferences on integrability since 2005 (in 2008: Utrecht, in 2009: Potsdam). Outlook: young people can participate in exact solutions of N=4 SYM theory for the first time. A few questions. One question was about multitrace operators. Answer: that's many chains, not been solved so far.

After the coffee break, Shiraz Minwalla (see fisherman and pole) continues by deriving nonlinear fluid dynamics from gravity: PDF here. ;-) Shiraz begins with the same energetic vibrations that you know e.g. from Superheroes haha. He specifically promotes two students of him, Bhattacharyya and Loganayagam. Sorry, I can't remember the exact names so far but I will surely learn them later: so far, copy-and-paste from SlavaM's comment was enough, thanks! ;-)

Shiraz explains that N=4 should have the 't Hooft limit, known from Maldacena 1997 to be IIB on AdS5 x S5. In the AdS/CFT map, local things may get mapped to nonlocal mess. However, he will show that in a sector, the right boundary dynamics is local.

To get there, he considers a general AdS 2-derivative theory, truncates it to AdS Einstein gravity. He will mostly prove the following map: all long-wave solutions of Einstein's equations can be mapped to Navier-Stokes equations solutions, with the values of transport coefficients determined holographically.

Two solutions are first examples: empty AdS and a boosted (by velocity "u") version of AdS Schwarzschild at temperature "T". The boundary stress tensor equals to a power of temperature times a general u-dependent tensor. For an arbitrary (time-dependent) stress tensor on the boundary, he defines Delta(x) - minimum length scale of variations - and epsilon = 1/(T.Delta). The question is what constraints for the stress tensor he can derive generally from AdS/CFT and Einstein's equations in the bulk. Nice.

Naively, tubes should connect the boundary points with regions in the bulk, i.e. with constant x_mu in Schwarzschild coordinates. Wrong, problems with causality, metric not regular. The first improvement are tubes that go along incoming geodesics. Surprisingy easy to implement, 15 linear differential equations come out. 14 are independent: 4 are constraints (conservation of the stress tensor up to an order; independent of fluctuations of "g") and 10 are dynamical (M g_n = s_n) with a source. Regularity of the future horizon has to be assumed. Together with one more assumption, the solution is fully determined. So the solution only depends on the temperature and velocity (and the metric), but not arbitrary functions you would have a priori.

So there's map between Einstein's equations and generalized (higher-derivative-terms-including) Navier-Stokes solutions. This includes higher-order terms and confirms the eta/s=1/4.pi value. Shiraz also says the word "RHIC" because Juan told me to say the word. ;-)

Their solutions are singular at r=0 but under some assumptions, it's shielded by event horizons - the unique null manifolds that reduce to the black hole one in far future. The holographic translation of the growing horizon area in the bulk is probably something like an entropy-density-current on the boundary, unless I am deluded. Various comments (too fast) which stress tensors agree up to the second order etc. Shiraz is speeding up, approaching the speed of light and the Planck frequency. :-)

A possible extension of their work is to (non-universally) add non-metric (gauge...) fields in the bulk i.e. charge densities to the boundary. In conclusions, generalizations should exist; turbulence should be dually found in gravity (rotating black holes); time-reversal-symmetry breaking; reinterpreting cosmic censorship in the hydro variables; some N^2 scaling. Thank you - and everything abruptly slows down to 1/100 of his rate. ;-)

Hirosi asks about the fate of Navier-Stokes singularities. Shiraz answers that one can't trust the solutions below the inverse temperature distance scale, if I am simplifying it correctly. Another question about causality: these problems only occur if you truncate the solution up to a finite order. Another question: what happens with the epsilon expansion above one? The map breaks down because of the extra 5th dimension in the bulk. Answer rephrased in terms of quasinormal modes, too: infinitely many new modes generate nonlocalities that are equivalent to the integrating out of many KK modes. Enjoyable talk.

Luis Alday talks about the AdS/CFT calculation of the gluon (N=4) scattering amplitudes (with Maldacena): PDF here. You have n gluons, L loops, infrared divergences, etc. Make them finite in 4-2.epsilon dimensions. I like his accent - similar to the Italian who went to Malta. Compare e.g. "finite piece" and "piece on the table" or "worldsheet" with the "sheet on the bed". ;-) He draws the disk for the amplitude and makes a duality that maps the problem to a Wilson line, I suppose, in the dual AdS5 space (as in the dual conformal symmetry). This is probably the key moment and he didn't explain it too well.

To show in practice, he considers a 2-to-2 scattering. Assume s=t, Mandelstam variables coincide. They reduce the scattering problem to finding the minimum surface that ends at a sequence of light-like segments. And it probably works. Not so fast. He gets IR divergences which is OK, he says (on both sides). The result, in a hypergeometric form, must be expanded in epsilon.

In the last five minutes, he shows some newest results, about the translation of Ward identities into dual Ward identities. Up to 5 gluons, things are determined, so he goes to n=6 and n=infinity. Explicitly, BDS Ansatz fails for n=6 - I suppose we have already heard it. The MHV amplitudes are related to Wilson loops. Because the calculations didn't depend on S^5 and fermions, he believes there's some universality here. Another hard task involves mesons - not solved yet but the singular nature has been understood. If you find a minimal surface for 6 gluons, Alday invites you for dinner. He also wants to reproduce the Gross-Mende trick here and repair the BDS Ansatz. The integrability hasn't been used here yet.

Cumrun Vafa says that the surface carries more information than the area - can you recover the shape from the amplitudes? Answer (not too interesting one): he's only interested in the area.

Finally, Andrei Starinets wanted to offer another talk about the application of N=4 to heavy ion physics (he disapproves my label AdS/QCD for him and his collaborators, stressing that he is doing exact science, but I will keep on using AdS/QCD for everyone who wants to apply stringy holography to the observable nuclear physics!), focusing on finite densities and low temperatures, but he slightly changed the topic to the holographic description of quark-gluon plasma.

After some remotely related words about AdS/QCD, he asks about the difference between proton-proton and gold-gold scattering. He shows a graph of energy density vs. temperature - growing up to some point and then almost constant. The task now is to compute the transport coefficients from the dual gravity: all of them should be included in the quasinormal spectrum. All of them (viscosities, diffusion coefficients) for N=4 have been calculated up to the first order (and mostly to the second order). E.g. eta/s is drawn as a function of lambda, ending at 1/4.pi. A numerical bug was recently fixed. Later, he was showing nucl-th physicists fitting a curve. There are now 3 mostly independent proofs of the eta/s=1/4.pi value=0.08. Various other systems are known to have higher values; QCD seems to minimize among empirically known systems.

Finally, he wants holography to teach us about quantum Bose/Fermi liquids. The specific heat scales like different powers of "T" at low "T". They have different excitations etc. Fermi liquids explained by Landau who died on the year when string theory was born (and Czechoslovakia occupied, as your humble correspondent adds): he's not sure about the significance of this discovery, and neither am I. ;-)

He jumps to some D7-probe Karch-Katz stuff, trying to compute specific heat at low temperatures and the charge density (retarded) correlator (of j0,j0), especially the poles. He looks for propagating modes, a new type of sound. He suggests that the holographic dual is a non-Bose, non-Fermi, new kind of liquid. To conclude, many things have been found already but more will be helpful for non-equilibrium QCD and ALICE at the LHC will bring new high-temperature data.

A question is what he means by holographic dual for hypermultiplets that make it weakly coupled in the IR. Not sure about the answer. After the talk, someone says that he meant ATLAS, not ALICE. I actually think he did mean ALICE - the Pb ions. But Starinets surrendered and said it was ATLAS. ;-)

Later, Andrei explained me that, of course, he wants ALICE, but he used an incorrect picture of ATLAS, and someone just told him (correctly) that the picture was incorrect.

Herman Verlinde began the afternoon session with holographic gauge mediation (of SUSY breaking), an AdS_5-like dual description of a hidden sector where SUSY is broken: PDF here. After a few sentences, the computer (Mac) started to behave funnily. Fixed. String phenomenology may be studied from the top down, from the bottom up (decouple gravity; see Vafa's talk and others), and to study strongly coupled theories that may be uncovered by the LHC. Imagine that the LHC finds some new technicolor/composite physics, with a new hidden sector. This sector couples to gravity, visible gauge fields, and other fields.

Herman now learned the two arrow keys. ;-) If the hidden mass scale is well above a TeV, integrate the hidden sector out and see the new soft terms. If the new stuff is light, you have to include it. Now, he apparently wants to study the AdS bulk dual of the hidden sector only. The visible fields (IR) define the boundary conditions of the AdS-like space; references to holographic RG. General gauge mediation by Maede, Seiberg, Shih is outlined. Klebanov-Strassler (i.e. conifold; SU(N) x SU(M+N)...) is now assumed to be the hidden sector. The dynamical nature of the SUSY breaking is reflected by normalizability of a mode. At least 5 D7-branes needed for a SU(5) global symmetry.

The gaugino mass is localized in the IR region of the D7-brane, separated from the Standard Model (stringy kind of "gaugino mediation"). This mediation may be obtained as a limit of gauge mediation with many messenger fields (thus enhancing one particular term). Such a large number will bring Landau poles closer, and this is a real problem visible in the bulk picture, too. You can trust this game in a small window only.

In the last five minutes, he wants some SM particles to be composite - "mesons" of the higher-energy theory. These fields now go to the bulk. One needs intersecting D7-branes. Among conclusions that repeat the stuff above, Herman recommends to study a merger of his idea - holographic dual of strongly-coupled hidden sectors - and Vafa et al.'s F-theory phenomenology. A Hirosi Ooguri's question is answered by saying that something was only true qualitatively, some backreaction was neglected.

David Shih talks about general gauge mediation, a paper also mentioned by Herman above. It's work with Maede and Seiberg (and another collaborator, Buican, a new paper in progress). He clarifies the comment that the LHC is behind the corner: it is actually across the street. ;-)

David will talk about SUSY because he believes it's the best motivated scenario for the LHC. It must be broken; in a new hidden sector; it must be communicated to the MSSM. He will focus on his preferred mediation, gauge mediation. It's communicated via MSSM gauge bosons which are flavor-blind, and thus the flavor-changing neutral currents are absent. The spectrum is viable, calculable, and predictively distinctive.

He wants to divide the predictions of gauge-mediated models to general and model-dependent.

David begins with "ordinary" gauge mediation from the 1990s (Dine, Nelson, Nir, Shirman). Keep only the X superfield (spurion) = M + theta^2 F. M breaks R-symmetry, the other F breaks SUSY. Superpotential X.phi^2 couplings create splittings; phi is in real reps of the SM. He gets 1-loop diagrams for gaugino masses and 2-loop diagrams for sfermion masses.

A slide already divides the features to general and specific. Gaugino unification, sfermion hierarchy, and identity of NLSP can be shown non-universal by a simple beyond-ordinary gauge-mediated model.

The hidden sector must generally breaks SUSY; contain messengers; decouple from MSSM in the g=0 limit. To look at the limit, assume the group G only, not the detailed dynamics. So what you can study are correlators of global currents (as in QCD before it was known). The current "J" is a whole real superfield. In components, he writes various 2-point functions as a function of x^2 in x-space. Some of them vanish for unbroken SUSY. Because the breaking is spontaneous, these coefficients must have a nice x=0, either zero or constant in one case or another.

He weakly gauges the G=U(1) group and integrates the hidden sector out. The last step changes the U(1) beta-function and generates soft masses in the effective action. Now, when he adds SU(2) and SU(3) to U(1), too, gaugino unification evaporates. Absence of FCNCs survives while CP-problems may occur. Sfermion masses were positive in all old examples but counterexamples (tachyonic) were found later. The typical momentum in the integral is M so you can't get it from low-energy effective field theory.

Sfermion masses are independent of gaugino masses as well as gauge couplings. A couple of sum rules seem to be general. Five different sfermions f=Q,U,D,L,E per generation are functions of three parameters A1,A2,A3, so there must be 2 relations: Tr(Y m^2) = Tr((B-L)m^2) = 0. Corrected by RG flow to the weak scale. To summarize, they have identified variables to study gauge mediation in general. They have 3 complex (gaugino masses) plus 3 real (sfermions) parameters. Can you cover this 9-real-dimensional parameter space by a simple model? Carpenter et al. have the right number of parameters but not sure whether they cover everything. Other tasks is to apply Herman's methods; and to solve the mu/Bmu problem, general for gauge mediation. The LHC will judge us.

It will inspire fear, put many models to the test, and most models to the rest. A picture of Terminator with the governor of California. A question: why something is small? Answer: because we say it is small. ;-) Later, he said it can be seen from 2-point functions. Cumrun Vafa says that to solve the mu/Bmu problem, he has to require more than one g=0, and David agrees. Simeon is too far, the echo makes it harder to hear. David says that they have no new solutions of the problem but he doesn't know whether a problem can be solved.

Romuald Janik will begin the last pair of lectures with comments on 4-loop (!) perturbative Konishi from the AdS5 x S5 sigma-model. Right before he began, an organizer noticed on my blog that Vafa, Maldacena, and Polchinski share the 2008 Dirac Medal, so there was some applause. ;-)

Romuald's beginning is motivation. He will define the Konishi operator, explain why 4 loops matter etc. The task is nothing less than to find spectrum of N=4 SYM for any 't Hooft coupling in the planar (large N) limit. He wants to do it in the light-cone uniform description of AdS5 x S5. One needs a very strongly coupled regime, so some integrability tricks will be needed.

The Konishi operator is Tr(Phi_i^2) summed over the six values of "i". He really wants to take Tr(Z^2 X^2) from the same multiplet. The known dimension looks like Delta = 4 + 12g^2 - 48g^4 + 336g^6 plus a horrible multiple of g^8 whose coefficient includes an integer, an integer multiple of zeta(3), and another of zeta(5). The four-loop result is interesting because it's the first one where the Bethe Ansatz breaks down (wrapping interactions) - a sensitive test how we understand the theory.

First he, extremely quickly, reviews the 1-, 2-, 3-loop results from the Bethe Ansatz. The 4-loop result is wrong here; the wrapping graphs that are missing have mess all over around the cylinder with the BMN-like operator at the circles at the boundaries. The spin chain is not useful because it is exactly equivalent to the Bethe Ansatz.

There are two ways how the virtual particles can encircle the cylindrical graph. One needs some relativistic rules to be generalized to non-relativistic worldsheet theories (relevant for AdS) and the whole stuff must be applied to the Konishi operator. The correction goes like an exponential; the exponent in the truly relevant case involves arcsinh. At weak coupling, he can expand to see that the leading terms are at 4 loops.

He's going to solve it iteratively by excited state TBA e.g. sinh-Gordon or SLYM. The 0th order are Bethe equations while 1st order corrections shift both momentum as well as energy (by an F-term of a sort). The momentum shift actually enters only at 5-loop. Also some poles may be neglected. So he writes the formula for "Delta E" only, the F-term. It's written as an infinite sum (over Q) of an infinite integral (over some intermediate momentum q) of some product of "S S" with many additional indices; "S" is the S-matrix. The "Q" labels magnon-like particle species that can run in the loops, including bound states. There are two types: su(2) bound states (symmetric representation) and sl(2) (antisymmetric, physical in the mirror theory). The latter sl(2) states should be used here.

The scaling is "g^8", of course, and the rest is computed via residues. The zeta-functions here explicitly arise here from the summation over "Q", the tower of bound states. Everything else turns out to be integer. And a full agreement with a Zanon et al. perturbative calculation is obtained.

When he looks at it, he finds the 324+864zeta(3)-1440zeta(5) surprisingly simple, not too transcendental. ;-) For su(2), he would obtain much messier stuff. He obtained the corrections in a way that is alien for spin chains but normal for 2D QFT. The agreement is a spectacularly nontrivial confirmation of AdS/CFT. A question was answered by an analogy with some Zamoldchikov papers.

Finally, Carlo Rovelli will try to convince the auditorium to unlearn, forget, and abandon almost everything they know (and said) about physics and jump to loop quantum gravity. He's very honored to be there and assumes that everyone is honored to see Rovelli. ;-)

He assumes that no one knows anything about LQG, which is probably not correct. The abstract suggests that the talk will be identical to the basic notions described e.g. in his review 10 years ago: you can make a career out of 5 page of nonsense that you keep on repeating for decades. What are loops, what is kinematics, dynamics here, and what has been achieved (not sure what he will say in this section). ;-)

Rovelli advertises his book and says that LQG is studied by 200 people. On the first slide, he claims that no new physics is needed and perturbative divergences of gravity are just illusions. This is all such a breathtakingly stupid case of wishful thinking that I might lose my patience and turn off the video, in which case I would apologize that this text is truncated.

He claims that general relativity is "two different theories" which leads to "misunderstanding between communities". I am afraid it will continue to lead to misunderstanding, very politely speaking. He offers some bizarre statement that fields in spacetime are something else than fields in geometry of spacetime, or something like that. It makes no sense whatsoever.

Fine, why loops? So he reminds the people of Wheeler-DeWitt and similar stuff and promises that loops solve everything. OK, why loops? Now, he could just say that they're open Wilson lines connected by gauge-invariant vertices. People in the room know how to calculate 4-loop terms in things like Wilson lines. Instead, he wastes the time of the auditorium (and mine) by confused presentation of some undergraduate stuff. Instead of saying what he means in one sentence (every other speaker would need roughly 5 seconds for this stuff - someone only 1 second which is too fast), he goes through basic lectures of lattice gauge theory. He is either unaware of the word "Wilson loop" or thinks that people around don't know what a "Wilson loop" is. How dumb this guy must be? Let me omit these trivialities.

In his opinion, Wilson lines in a continuum are "too singular". Well, it depends. Then he claims that two previous problems cancel against one another because diffeomorphism invariance removes the "singular" nature of the space. It is easy to see that it does not (once you try to add *any* dynamics). He continues with some elementary stuff about "connections" and "Ashtekar variables". I am convinced that most people in that room have heard about these things already. Sorry, I have heard this very same stuff about 15 times already; they think that by constant repetition, they can imprint some nonsense to someone's or everyone's head. Except that this is not how it works in science.

Childish slides about "loops" and "strings" being both 1-dimensional follow, together with wrong statements that he can define the volume operator on his Hilbert space. It's known that you can't, it's singular (unlike the areas). He also says a lot of wrong statements about the finiteness of the Hamiltonian. See e.g. Nicolai et al. 2005, the most cited LQG paper in 2005, that explains that these things cannot be well-defined (without an infinite number of continuous ambiguities).

When he tries to talk about the path integral (spin foam in his case), he spends several sentences about Feynman's thesis, apparently assuming that the participants have probably never heard about the path integral. His talk is clearly not addressed to experts of any kind and he has clearly no idea what the physicists in the room are doing, not even approximately.

"Loop cosmology" is mentioned as an "application" of this pseudoscience. The usual misconceptions about the "removed singularities" are repeated. Nothing like that is removed, however. The infinite-dimensional dependence on the cutoff remains both in LQG and loop cosmology; it is only translated to the infinite-dimensional uncertainty of the Hamiltonian, just like in any other case of brute force cutoff regularization. Untrue statements about black hole entropy are added. These people are simply liars. They must know that what they're saying is just not true because there are hundreds of papers showing this fact with complete clarity and they must have seen at least some of them.

Simeon Hellerman asks what the can Rovelli possibly mean by a "black hole" if he doesn't even have the right low-energy limit (whose solution the black hole normally is defined to be). The second question is about the coefficient 1/4 and its universality (which is known not to be universal); Rovelli only admits that it is an issue. Concerning the first question, Rovelli talks about different definitions of horizons - which is completely irrelevant because he can't apply any definition of the horizon if he can't localize the Einstein-Hilbert limit with the smooth space in his Hilbert space.

Someone else says that Rovelli is in a topological phase - a polite way of saying that he incorrectly treats the groups. In the proper treatment, one gets the gravitons from reducing diff to the Lorentz group; gravitons transform under the latter. Rovelli tries to prove that a theory that satisfies all the group properties of a topological theory is not topological. ;-) Michael Douglas asks whether the LQG people have tried to make a contact with the important advances in 3D gravity by Strominger and others (much more solvable). Rovelli has, of course, no idea about the work going on in actual physics, in 3D, 4D, 10D, or any other dimension. He has only heard a remotely related 3D talk by Maloney. So somebody should sit down, he says.

Someone else asks why they could change the value of the Barbero-Immirzi parameter, from Penrose's gamma=i to ln(2)/sqrt(3).pi or something like that (see the quasinormal story on quasinormal modes). Rovelli says that "gamma" is analogous to theta_{QCD} and the value in the quantum theory should be carefully chosen. It's no contradiction, he says. Of course that it is a contradiction because they either obtain a wrong value of the black hole entropy or a wrong Newton's constant at low energies (assuming no divergences and flowing, as he likes to say). Another question is from a person who knows that LQ cosmology cannot be derived from LQG: it is not a reduction. Rovelli admits it cannot be derived, except for hand-waving (randomly modifying the theory). Thank God, it's over. Applause.

Monday, Tuesday, Wednesday, Thursday, Friday

Warsaw Pact occupation of Czechoslovakia: 40 years later

Video 1: Pictures mostly from Prague. The sound features (otherwise patriotic) radio hosts who are telling the people that it makes no sense to resist physically because the invaders are far too strong - a theme about "adaptation" that we've known at least since 1938. ;-) So Czechoslovaks were at least trying to twist the traffic signs to confuse the foreign soldiers and inventing anti-Russian jokes: see another (moving) video. Prague became the most civilized city in the world to be occupied by tanks since 1945.

See also: Obama's 4-minute speech about the anniversary

Exactly 40 years ago, in the early morning of August 21st, 1968, the Warsaw Pact tanks invaded Czechoslovakia, occupied the country in a perfectionist Blitzkrieg operation, and ended the Prague Spring, a period of democratization, liberalization, and socialism with a human face.

I deliberately didn't say that it was the Soviet troops. Among the 200,000 troops, you could find 28,000 Poles - quite a huge percentage. The Russians were only a majority because they were a majority in the Soviet bloc, too. Besides the Soviet Union and Poland, the other countries that participated were Bulgaria, East Germany, and Hungary. Ceaucescu in Romania refused to send troops, and so did Yugoslavia and Albania (the former was the only country that mobilized, in support of Czechoslovakia, thanks a lot, while the latter left the Warsaw Pact because of the incident).

The utopia of democratic socialism

Around the middle 1960s, Czechoslovak communism started to "soften", in a huge contrast to the brutal executions and fundamentalism in the 1950s. Perestroika-like economic reforms were adopted: Mr Ota Šik of Pilsen was the architect of the new economic plans. In 1968, Mr Alexander Dubček [pronounce: Doop-Czech] of Slovakia was chosen as the new boss of the communist party and democratization began, too. Free press and hundreds of types of activities started to flourish. This year is referred to as Prague Spring.

You should realize that the Czechoslovak economy of the 1960s was still comparable to the Western economies and a smooth transition to capitalism - that could naturally follow from the democratic socialism - could abruptly return us to the Western world where we belonged for the previous millenium.

The "nice" communists were, of course, dreaming about the preservation of communism, just making it human, efficient, and so forth. Today, it is widely accepted that such an idea was a utopia. Socialism is inherently incompatible with democracy and freedom. Socialism has to mess up with basic mechanisms regulating a free society: it wants to create unnatural conditions. To do so, it must always adopt some totalitarian techniques, to one extent or another. But a democratic socialism could have been just the first step towards normal democracy and capitalism, of course.

In my opinion, Dubček was a decent, likable guy but a naive politician. After the Velvet Revolution in 1989, he was naturally a possible candidate for the president of Czechoslovakia. But there were all kinds of problems with him because his speeches still sounded like communist speeches, in a sense. When Dubček learned in December 1989 that Václav Havel was chosen as the Civic Forum's presidential candidate instead, he started to cry like a small girl. He was not ready for real competitive politics in a democratic country. A few years later, he died in a car accident. As a yellow cab driver in Boston once told me, he was killed by the "multi-nationals" :-) which sounds funny but what do I know?

Getting ready for the occupation

What happened before the occupation began? As we learned in the early 1990s when former President Havel was given some secret letters from the Russian government, five Czechoslovak communist traitors (Biľak, Švestka, Kolder, Indra, and Kapek) wrote a letter to the Soviet authorities claiming that

"... right-wing media [were] fomenting a wave of nationalism and chauvinism, and [were] provoking an anti-communist and anti-Soviet psychosis." It formally asked the Soviets to "lend support and assistance with all means at your disposal" to save the Czechoslovak Socialist Republic "from the imminent danger of counterrevolution."

Mr Biľak gave another version of the letter to some Ukrainian guys, during a meeting organized by KGB. Well, these were important enough communist puppets for the Soviet (and other) politicians to act. I kind of understand that they did. In this sense, I prefer to blame the Czechoslovak traitors more than the foreign communist politicians. But the very communist system was the primary reason why these events took place.

I will never accept the nationalist, anti-Russian interpretation of all these events. The Prague Spring and the occupation that followed were about the tension between the freedom and totalitarianism. The totalitarian ideology has been connected with all kinds of nations. Marx was German, Lenin was Russian, Stalin was Georgian, Mao was Chinese, and Che was Argentine. Czechoslovakia always had its own communists who were the key for the rise of hardcore communism both in 1948 and in 1968.

Moreover, Russia has done good things for us, too - including the liberation of most of the country from Nazism in 1945. In my opinion, currently fashionable inherently anti-Russian positions (that moreover judge two isomorphic situations very differently, depending on the role of Russia in these two situations) are analogous to the German anti-Semitism during holocaust: they are racist in essence and I am shocked that the people with those opinions don't realize it.

The defeated player in the Cold War was communism, not the Russian nation, and as soon as Russia adopted its kind of democracy, the "reparations" have been paid. There exists no justification for an additional "punishment" against Russia. I have a lot of respect for numerous people who enjoy their childish anti-Russian image but when it comes to wars (such as the recent war of Georgia against South Ossetia that backfired, as wars often do), it's just damn too serious if someone is not able to judge the situation fairly.

Pat Buchanan writes about the natural reactions of a provoked bear: I agree with him completely

But let's return to the events in 1968. After the invasion, freedom, optimism, and national pride were slowly dying away. A few smart students burned themselves to protest against the Czechoslovak defeatism. Some people were thrilled in January 1969 when Czechoslovakia beat the Soviet Union in ice-hockey and they destroyed some Russian interests in Prague. ;-)

Of course that the anger used to have anti-Russian dimensions, too - but one should appreciate that the sentiment was mostly against the Soviet establishment as it existed at that time, not necessarily against the Russian DNA (that we partially share, anyway). By the early 1970s, the period of the so-called "Normalization" - a return to neo-Stalinist conditions and nearly complete stagnation of the economy - was firmly in place.

The occupation was suddenly referred to as "fraternal help" while the Prague Spring became a "counter-revolution attempt". This vocabulary was summarized in the "Lessons from the crisis development in the party and the society after the 13th gathering of the communist party", a propagandistic text written by the same Mr Biľak, the party's ideologue. About 300,000 people emigrated from Czechoslovakia right after 1968 and most people connected with the 1968 events were fired from jobs and schools.

For me, the occupation itself is of course just a chapter from the history textbooks and a part of my "initial conditions". I can't really blame those communist guys because if they hadn't done what they did, I wouldn't be here. Gustáv Husák, the new (Slovak) neo-Stalinist president of Czechoslovakia, established many new (not always catastrophic) policies, for example new pro-population-growth policies (support for new kids) that led to the birth of many "Husák's children" around 1974. Your humble correspondent is one of them. ;-)

Comparisons with other events

Some people compare the Warsaw Pact invasion of Czechoslovakia e.g. to the recent Russian actions in Georgia. I find such analogies kind of insulting. While I have voiced some complaints against Mr Dubček, he was an extremely peaceful guy, a naive, grown-up kid. Unlike Mr Saakashvilli, he didn't occupy Ruthenia before the invasion of our "allies". No Russian citizens were threatened anywhere in Czechoslovakia. The 1968 invasion was an action of totalitarian countries meant to destroy a newborn democracy in another country while the recent events in Caucasus are just battles between several comparably democratic countries, driven by their territorial interests. These are huge differences.

Lessons

The occupation has shown that socialism has no tolerance - and cannot really have any tolerance - for internal diversity of socioeconomic systems. In some sense, the communist guys had to act if they wanted to avoid an abrupt decay of socialism in Europe (that we saw 21 years later). Socialism is an inherently totalitarian ideology. The occupation showed that it is, of course, possible to use brute force to change the fate of a country for several decades. But when the system is not built by the local people, they will never consider it their own system.

I think it is not really possible to "export" political values by force. To some extent, I think that this comment holds for the export of democracy, too. Whenever democracy started to flourish (e.g. in West Germany after the war), it was in a place that has had some experience with it.



By the way, today, in Olympic female javelin, there were only two serious contenders (besides all the amateurs): Abakumova of Russia and Špotáková of Czechia. Abakumova was ahead of Špotáková throughout the game (by 10 centimeters only). But the last throw of Špotáková changed everything: over 71 meters, Europe's new record. She earned the golden medal. She said that she was thinking about the occupation, too. So far, she is the only one who both promised and earned the gold medal. It's the third Czech gold medal and the sixth medal in total at these games. One gold medal and one silver medal was earned by Mrs Kateřina Emmons, a fellow Pilsener who married a fellow shooter from the U.S., Matt Emmons.

Strings 2008: Wednesday

You may go to the main Strings 2008 page on this blog; that page includes the live webcast

Lance Dixon starts the morning session (the only one today) by a talk about the structure of gauge-theoretical and gravitational scattering (on-shell) amplitudes: PDF here. (See also a text about his talk on transcendentality and about his SUGRA puzzle on this blog.)

Jester at Resonaances dedicates a text to Dixon's talk, too.

A ten-minute delay was caused by repeated trouble with the Mac. Couldn't they train the technology in advance? Dixon's title page has various Feynman diagrams and boxes divided to smaller boxes and his first sentences were compliments to CERN and the conference. He plans to talk about QCD for the LHC (with many external particles and many loops), N=4 and AdS/CFT, and finiteness of N=8 SUGRA.

He explains that on-shell amplitudes are more physical, independent of field redefinitions and gauge choices. They may have hidden structures that are only understood later, e.g. the MHV amplitudes (clarified by twistor string theory). Infrared (physical) divergences are often a part of the story, making things complicated but doable (describe them by jet functions).

His big message is that the amplitudes are "plastic" - he means various factorizations well-known to string theorists (with Riemann surfaces). Unitarity determines discontinuities across branch cuts, too. These features - together with the helicity approach - may be enough to determine the amplitudes. Mantis shrimp have different reflections and sensitivities for left-handed and right-handed photons: they are able to communicate via helicity formalism and only theorists understand these shrimp (other animals and experimenters are blind). ;-)

He reviews 2-spinors and their products, including the <12> and [34] notation we know from the twistor minirevolution. It's important to know how to continue momenta to complex values because for complex momenta, one can make various polynomials of momenta vanish without being pushed to singular collinear configurations. Britto et al. (BCFW) 2005, shifting the spinors around and deriving the recursion relations for amplitudes from some residues in contour integrals, is reviewed. It's an environmentally, politically correct way to calculate because the trees are recycled. ;-)

For 6 gluons, instead of 220 Feynman diagrams, you have 3 terms, one of them vanishes and the other two are mirror images of each other: really 1 contribution is here. Like in Olympics he watches, difficulty increases with the number of loops and legs. ;-) The style also matters but it is more subjective - for example, he cares about the proximity to experiments. The difficulty index decreases with the number of supersymmetries. He draws many papers into this 2D graph spanned by (legs, loops).

At the LHC, we should understand QCD with many partons and a couple of loops: complicated SM backgrounds - as Oliver Buchmüller was explaining in the context of the "SUSY" signals with cascade decays. One-loop amplitudes are then decomposed into a rational term and a singular one (with cuts). The singular term is decomposed into a combination of standardized functions with poles. A useful concept is generalized unitarity - with cuts where not 2 but 3 or 4 particles are on-shell. Britto, Cachazo, Feng 2004 were able to split a "box" coefficient in the decomposition into an integrated product of four tree amplitudes. One can explain why no pentagons appear.

Besides boxes, one must look at triangles and bubbles. Nice pictures but I don't think he explained the machinery - the reorganization of the diagrams - too well. The next question are the rational terms of the 1-loop amplitudes. Unlike a dozen of other papers, his strategy is to use plasticity, recycling trees and loops again. CutTools, Rocket, and Blackhat are three state-of-the-art programs to calculate 1-loop amplitudes. Rocket goes up to 20 gluons.

Now he gets to multi-loop & multi-leg diagrams, pointing out that things are similar for N=4 SYM and N=8 SUGRA, due to the stringy KLT relations. So he's dissolving very complex diagrams now. After he finishes a procedure, he talks about some "missing diagrams" (near-maximal cuts etc.). It's not clear whether their procedure is systematic and leads to a full answer or whether it is just heuristics to guess some singular parts of the answer.

Some elementary facts about AdS/CFT and planar limit of N=4 SYM follow. Interesting related things occurred in N=4 SYM: exponentiation of finite terms, dual superconformal invariance, and a MHV-Wilson_line equivalence. Exponentiation: the ration of an amplitude and its tree part is naturally an exponential of a simpler expression. The simpler expression, a sum, only depends on the kinematic variables through some one-loop amplitudes. This surprising Ansatz was shown to work for 4 gluons, indirectly for 5 gluons, but it is known to fail above 5 gluons. If some promising conjectures are right, one could explicitly write the full 4-gluon amplitude.

Dual conformal invariance is shown using a box diagram with 4 gluons. Write the Feynman integral over momentum. Now, the point is to look for conformal transformations acting on the momentum space and not x-space as usual. Among conformal transformations, the spherical inversion is a sufficient generator (with translations). Cutely enough, straightforward rules are known to decide whether this invariance under inversion holds. And it does hold 4-gluon amplitudes at 1-loop, 2-loop, 3-loop, 4-loop, 5-loop level. ;-)

This symmetry sounds crazy. Where does it come from? String theory, of course, namely a T-duality of AdS5 x S5 and Wilson line calculations (that seem helicity-blind, however).

The Ansatz should work not only for 4 but also for 5 gluons. It is known to fail for 6 or more gluons - there are new invariant "double ratios" - but the dual conformal symmetry and Wilson lines are still there.

Finally, he jumped to hidden cancellations in N=8 SUGRA. Up to 3 loops, it has been shown that, as hinted by KLT relations, the N=8 SUGRA is as finite as N=4 SYM. The 3-loop integrals include 9 Feynman diagram topologies (2 of which are new). Full calculations may look tough but the "equal finiteness" as N=4 SYM is manifest. Whether or not the theory is finite to all orders is an open question, he says. Conclusions repeat some points above.

A question asked him about the Ansatz extending 4 gluons to 6 gluons or more. They're working on it: not yet. Very nice talk.

Michael Green is following with a talk about the constraining power of supersymmetry combined with dualities in (type IIB) string theory and supergravity: PDF here. See also Two roads from N=8 SUGRA to string theory. He will talk about the perturbative finiteness, too.

First part: he shows a derivative expansion of low-energy actions in string theory and reviews the type IIB massless fields. He explains why the moduli space is SL(2,R) \ SL(2,Z) / U(1); it can also be seen from a U(1) anomaly in the SUGRA framework. Only SL(2,Z) is the symmetry of the quantum (string) theory. Terms in the action, F, are not holomorphic. How are they constrained by SUSY? The constraints are hard to illuminate without a superspace formalism.

The closure of SUSY schematically requires "DF = F + FF + FFF ..." with all kinds of indices and coefficients. It is also useful to add "Dbar" to the equation, to obtain a Laplace "eigenvalue" equation - that can be solved by "F = Eisenstein series", generalizing the Riemann zeta function. By SUSY, he can conclude that the R^4 term only comes from the 1-loop term, multiplied by E_{3/2} (Eisenstein). Similar for other terms at other loop orders.

The four-graviton amplitude is now expanded in alpha', starting with the beautiful Virasoro-Shapiro amplitude that can be expanded. The expansions of higher-loop amplitudes are tougher. Green expanded various amplitudes, showing the coefficients being products of zeta functions.

Finally, he jumps to the relationship between SUGRA (M-theory on tori) and type IIA, IIB string theory: the radii must go to zero in various ways to get the limits. Green kind of assumes that SUGRA may need perturbative counterterms. However, he says that some of the terms may be determined from string theory. The elegant mapping is explained, for a 2-loop case, by mapping a real torus to the auxiliary torus.

Green skipped a few pages of details and gets to the loops in SUGRA. To study the divergence structure, he wants to look at the powers of S at various loop levels. The exponent is known up to 3 loops; higher powers of S make the expressions more convergent. Because 3-loops begin as S^3 R^4, S^2 R^4 can't be renormalized beyond 2 loops - e.g. a five-loop counterterm of this kind has to vanish. Similarly for other terms with other number of loops.

To summarize, one of the conclusions is that they argue that there's no divergence up to 9 loops. Green suggests that it might be that it holds to all orders, too - having the same degree of divergence as N=4 SYM.

If that's finite, why were we doing string theory? So he reviews his work with Ooguri and Schwarz: you can't decouple SUGRA from string theory because in any limit, there is a tower of states that is light. Perturbative finiteness doesn't imply finiteness. The final slide is a joke that the going to higher orders is speeding up, and one can resum it to show that we will get to "L=infinity" loops by 2014. ;-)

Juan asked about some relationship between the divergence structure in 4D and 10D. In 10D, things are very divergent. Both in 4D and 10D, there's an anomaly that prevents U(1) to be the exact symmetry, Green says. Nice.

After the coffee break and a few announcements, Freddie Cachazo speaks about the simplest quantum field theory, which is their new label for N=8 SUGRA (work with Kaplan and Arkani-Hamed): PDF here. The main "simple" feature of the S-matrix of this theory are amazing convergent properties of the amplitudes at an infinite complex momentum. Tree level amplitudes are determined by Lorentz symmetry (3 particles). One-loop and higher-loop amplitudes are all determined by the leading singularities.

Be careful: asymptotic/nonperturbative corrections are still large at trans-Planckian energies, E7 must be broken to the discrete subgroup, and so on.

So Freddie returns to the S-matrix programs of the 1960s. It was all hard - but only because they looked at hard theories. They should have looked at N=8 SUGRA, back in the 1960s. ;-) At least, we can do it today. Freddie begins with the 1-complex-parameter deformation of the amplitudes: momenta are shifted by a multiple (z times) a momentum "q" which is (0,0,1,i). Here, q is null. The amplitude "M" becomes a rational function of "z". By contour integrals, it goes like 1/z^J for spins J=0,1,2, so to say. Gravity falls faster than scalars and Yang-Mills, in this complex direction!

Why? In this novel complex infinite momentum limit, one finds a new symmetry - the so-called "spin symmetry" - that decouples Lorentz indices from the derivatives. Gravity has twice as many indices relatively to gauge theory, so it goes like 1/z^2. If gravity is so nice, why do they add SUSY? Because without SUSY, unitarity leads you to combine the "very convergent" amplitudes with other, "divergent" z^2 amplitudes. With SUSY, all of them are related. So "everything" is smooth and nice in "z".

In fact, he can define the N=8 SUGRA S-matrix without any Lagrangian, just with some Grassmannian coherent states. Scalars didn't vanish in the past. So he modifies the 1-parameter transformation of BCFW: also the fermionic variable is shifted by "z" times something, bringing the decreasing behavior of gravity to the whole multiplet.

Now, he wants to see nice things like the E7(7) symmetry from their S-matrix that was produced from Lorentz symmetry and the complex tricks only. Of course, the moduli space is seen from a soft behavior of single soft emission of scalars. (Gravitons are divergent.) The double soft emissions seems to show a paradox. It is explained by seeing that a limit is finite but depends on a regulator, the direction, and the structure of it encodes the E7(7) symmetry. I haven't quite understood it yet.

At the tree level, the only singularities are poles. However, cuts appear at one loop. The log^2 functions here have a discontinuity of the log form which is itself discontinuous (and appears at quadrupole cuts). This discontinuity of discontinuity is thus seen near the highest-codimension branch cuts and the whole amplitude is fully determined by the behavior near this special point, i.e. by the leading singularity.

He finds that triple cuts are determined by quadruple cuts, and double cuts are determined by triple cuts (no new singularities). So everything at one-loop is really determined by the quadruple cuts. The no-triangle hypothesis is rephrased in a new way here. Everything is included in the scalar boxes.

At L-loop level, one cuts 4L propagators instead (very many!). Sounds crazy but anyway, the whole perturbative N=8 S-matrix is determined by the leading singularities. This is equivalent to the UV finiteness: if a part of the S-matrix is not determined by the leading singularity, there must be a divergence.

To summarize, he wants the leading singularity conjecture to be proven, find the explicit action of E7(7), and try to go above d=4.

Simeon Hellerman complains that it can't be true that SUSY and Lorentz determine everything because one could add any N=8 invariant counterterm. Freddie says that such new terms wouldn't spoil the behavior at infinity. Lance Dixon thought that some singularities could still appear in the denominator but Freddie insisted they would cancel. Another question was about the relation of E7(7) and its continuity beyond the tree level and Freddie said "Yes, yes" but didn't quite clarify the situation.

Nathan Berkovits explains one trick that has emerged in his pure-spinor analysis of AdS_5 x S^5: namely the fermionic T-duality: PDF here. He found it with Juan Maldacena. A dense slide with formalism follows immediately. ;-)

A T-duality of the AdS5 x S5 maps the NS-NS fields well but the 5-form field strength is not behaving well. However, the latter is subleading for large radii. Moreover, it can be completely fixed by adding the fermionic T-duality: then it works for all, not just large, 't Hooft coupling. Shockingly enough, this thing hasn't been considered before even though it is a direct extension of the bosonic case.

Nathan reviews the bosonic T-duality, following the Buscher rules. The action is invariant under a shift of a boson - that only appears with derivatives in the action. One can add Lagrange multipliers to get an equivalent theory if one variable is integrated out; if you integrate A instead, you obtain the T-dual theory.

For worldsheets with cycles, the "A" can have "Wilson lines" and one must be careful about the compactness of X, Xdual. The periodicities are inversely related. For open worldsheets (and open strings), the Neumann and Dirichlet conditions are interchanged.

To get a fermionic counterpart, the "isometry" fermion must be a worldsheet scalar. So the RNS picture is no good but the Green-Schwarz, pure spinor, and hybrid formalisms are fine. The fermionic Buscher procedure is almost identical and the differences can't be easily written without equations. Again, two ways to integrate things out exist.

This T-duality works on simply connected surfaces. At worldsheets with cycles, one can make the fermion "multi-valued" but the details are subtle. The fermionic periodicity must be a zero mode that must be integrated over. That's really strange. Is that integration added ad hoc to the stringy rules for the S-matrix? That would probably spoil unitarity. The Dirichlet/Neumann boundary conditions are now not switched.

Now, he would like to expand the superfields in the components (spacetime fields) and see how they transform under the fermionic T-duality separately. The T-duality transforms a SUGRA-equations solving background to another background solving them, and replaces the original fermionic Abelian symmetry by another one.

Example 1 involves 4D Minkowski space times a Calabi-Yau 3-fold in the hybrid formalism. He needs a coefficient of (d theta)^2 to be nonzero which can be achieved by a harmless surface term. Not clear what the physical interpretation of this new duality is. Too much formalism here.

Example 2 is the AdS5 x S5 as a GS sigma-model, with 4 bosonic and 8 fermionic translations ready to be T-dualized. The dilaton doesn't transform: the fermionic contributions to the gradient cancel against the bosonic ones. The dual conformal symmetry that should be explained by the fermionic T-duality is sketched - too quickly to learn it. To summarize, one has a new symmetry, one that works for the tree (meaning genus 0 = planar) amplitudes only. He wants to check other backgrounds and extend the transformation to a fermionic U-duality. I am confused what it means if this operation only works at the tree level while U-duality relates strong couplings with other things.

I had almost no chance to understand the first question. ;-) But the answer is that one can make a sequence of several fermionic T-dualities and they commute in all his examples: he only knows what to do with Abelian supergroups. Another question was answered that he doesn't know whether one can go beyond genus 0. The last question had no known answer. Interesting stuff, indeed.

Emery Sokatchev has a related talk about the dual superconformal symmetry of the N=4 scattering amplitudes, a topic mentioned by Nathan, Juan, Lance, and others: PDF here. A review similar to a slide by Dixon (about IR divergences etc.) appears at the beginning, together with a few words on MHV amplitudes.

The dual conformal symmetry only works at the planar level - it must therefore be dynamical, invisible at the Lagrangian level. It effectively acts on the momentum space - more precisely on a fictitious x_{i,i+1}-space obtained by a field redefinition in the normal momentum space (no Fourier transform). Here, this "x" is inserted in between the external momenta p_i and p_{i+1}.

The vev of the Wilson loop with carefully engineered cusps, according to the momenta, is proportional to the scattering amplitude.

The dual conformal symmetry is directly relevant for MHV amplitudes - unfortunately, I completely missed what the relevance is. Did he say it? But he already asks about the non-MHV amplitudes. I am getting lost because the difference between things that are new and things we normally know is not highlighted too clearly. I suppose that he is now reviewing some well-known scalings and degrees from the helicity formalism. The MHV amplitude is factorized, to keep track of all the infrared divergences. Fermionic coordinates are added to the dual space, to extend the dual conformal symmetry to dual superconformal symmetry.

Moreover and however, I have to go now, sorry.

Monday, Tuesday, Wednesday, Thursday, Friday

Oslo 2008, 33rd IGC: geologists are skeptical

Last week, Oslo (Norway) was hosting the 33rd International Geological Congress:

33rd IGC Oslo 2008 (main website)

They have talked about diverse topics related to geology and there are many interesting videos available on the website. But if you have 66 spare minutes (and Windows XP with Microsoft Internet Explorer), I specifically recommend you a panel discussion on climate change that took place on 08/08/08:

Panel discussion (webcast)

Henrik Svensmark and Bob Carter were on the panel and Bob Carter in particular has said many wise and nicely organized things over there. Most geologists who spoke from the audience were skeptics, too.

Various participants of the conference have criticized the notion that the climate is still warming (how many cooling years do we have to witness to stop saying that?), Al Gore, IPCC and its lack of open-mindedness, unreliable climate models, especially when it comes to clouds (Svensmark), the opinion that sea levels are accelerating, and so on: see RightSideNews.

Rasmus Benestad is nervous about the conference and wrote a text attacking the "contrarians", apparently not realizing that it is him who is the contrarian here. Not surprisingly, geologists have been denounced as puppets of the oil industry by the RealClimate.ORG faithful and everyone is happy again. ;-)

Strings 2008: Tuesday

First, great news from the world of awards.

Wikipedia pictures above were taken by your humble correspondent

Joe Polchinski (KITP, UCSB), Juan Maldacena (IAS Princeton), and Cumrun Vafa (Harvard University) joined other well-known physicists and won the 2008 Dirac medal for their stringy discoveries. Congratulations! But back to Strings 2008.

See also the main page about Strings 2008 on this blog... The PDF files are also available at the Strings 2008 website

Luis Ibáňez started the Tuesday morning session by a talk about string phenomenology (PDF here). We all believe that string theory unifies gravity and particle physics but can the SM be embedded and can we predict new things? We will have to use the data (LHC, cosmology) to restrict the possible compactifications. He shows the 1995 duality hexagon of M-theory and adds some structure in it, insights until 2008 (D3-branes, G2 holonomy, RCFTs etc.). The region outside is now called swampland. ;-)

He distinguishes global and local models - global ones are complete, local ones only care about a vicinity of some point in the extra dimensions. The latter incomplete approach is useful and is pursued by many big shots. (At this moment, the Mac starts to misbehave. Beep beep beep and Ibáňez, as an anti-Ellen Feiss, tries to switch to Windows.) That includes D-branes at singularities.

In mapping the MSSM landscape, he begins with the E8 heterotic orbifolds. Pure MSSM can be obtained, gauge coupling unification is likely. Heterotic Calabi-Yaus follow: Wilson lines needed to break to the Standard Model. It's even simpler to eliminate non-MSSM matter.

In type IIA, one combines intersecting D6-branes with orientifolds. The well-studied orbifold constructions involve Z2 x Z2 but recently people found Z6 examples, too. A problem is SM adjoint matter. Mirrors of these models involve magnetized IIB branes.

About 210,000 type IIB Gepner-like RCFTs have been found to resemble the MSSM. Pure MSSM with no exotics can be found. These models probably correspond to too special points in the space of vacua. In type IIB, one can also consider D3-branes (and probably also D7-branes) at singularities.

Finally, GUTs may be found in local F-theory (type IIB-based) compactifications, following Vafa et al. (as discussed right below Ibáňez's talk). New spectrum absent in normal IIB is possible, including spinorial matter and exceptional gauge groups. The GUT is broken to SM by magnetic fluxes. The picture seems to be rather unique.

A table summarizes the successes of the classes - B-L, absence of exotics, gauge coupling unification, fixed moduli. None of them gets an "A" in realistic Yukawa couplings as of now. So we're "not there yet" in getting the complete SM.

He looks at some landscape statistics - which doesn't mean that he adopts the anthropic selection criteria (calm down, please). He believes that some adjoint matter etc. is only light because we're looking at the orbifold points. We don't know whether low-energy SUSY is "generic". (Well, "generic" is something different than "predicted" by the theory, but OK.) He looks at the Yukawa couplings, stressing that non-perturbative contributions may be crucial. Examples of brane instantons in intersecting braneworlds follow.

Fluxes have been known to fix the moduli for 5 years or so (somewhat bizarre references for this fixing). A better control is obtained in large-volume models with multiple separated Kähler moduli. In type IIA, one can stabilize the moduli without instantons (Kähler and complex structure moduli co-operate). And the bulk of the landscape could be non-geometric.

What is the string scale? When it's 1 TeV, it's cool with all the Kaluza-Klein, stringy, black hole signatures at the LHC. More likely, when it's at the GUT scale, SUSY can be at 1 TeV. SUSY breaking has to be calculated and is not easy.

In string theory, it can arise from closed string fluxes, dynamical breaking in a gauge sector. Also from gravity, gauge, anomaly mediation (and mirage - perhaps natural in KKLT...). They each have advantages and disadvantages. The LHC should tell us something about it here. Type IIB has no Kähler moduli dependence of the superpotential, unlike type IIA.

There are three different very predictive types of SUSY breaking of some kind where all the superpartner masses are determined by one dimensionful (and a few known dimensionless) parameters. Intersecting 7-branes give us a very clear pattern. Stau tends to be the LSP but it can be fixed.

The LHC will tell us something about the string theory vacuum. If low-energy gravity works, great. If SUSY is found, extremely good. The only pessimistic scenario is that only the Higgs is found: the anthropic explanation of the electroweak-Planck gap will gain power. Also, unexpected surprises are possible. In a few years, the hexagon of M-theory will be covered by overlapping new circles of LHC and cosmology constraints - the right class but probably not the right exact vacuum may be located. A very good talk!

Cumrun Vafa mostly uses colorful tablet-PC, partially hand-written (maths and pictures) slides (PDF here). Very readable. (I was fixing his tablet PC as well as laptop once haha.)

He starts his talk about F-theoretical phenomenology by our goal to find the theory of everything. He finds anthropic explanations unsatisfactory while the goal to find the full exact theory hard. To solve the first (anthropic) problem, he prefers to search for the keys under the lamppost ;-). To solve the second part, he has to look for parts: a justification of the "local models" follows.

Cumrun refers to the SM-like sector as "open strings" and the gravity sector as "closed strings". So we focus on the vicinity of the place where the SM lives. One must assume that gravity decouples from the SM: that can be false but it's healthy to try. This assumption implies, for example, that the GUT must be asymptotically free so that gravity may have been postponed to higher-than-Planckian energies by Nature.

Interesting matter-carrying branes must be SUSY-like, i.e. wrapped on 2, 3, or 4-dimensional cycles. He thinks that the higher-dimensional branes are more flexible which is why he chooses 3+4 = 7-dimensional branes, leading him to type IIB.

Another input is a SUSY GUT-like unification. He views the pretty and natural representation theory of GUT to be stronger evidence supporting GUT than gauge coupling unification. Now, gauge groups like SO(10) are easy in type IIB but the spinor seems impossible (much like the top quark Yukawa coupling) so he must go to (va)F(a)-theory, non-perturbative IIB (his brainchild), where all problems are solved. Cumrun is shocked that his cell phone is able to interfere with the microphone or speakers (noise!). I've learned this thing a few months ago (experimentally). ;-)

There's a nice even-dimensional hierarchical structure here: gravity lives in 10 dimensions, gauge fields in 8 dimensions, matter fields in 6 dimensions, and interactions in 4 dimensions (the intersections).

The SO(10) spinor arises from a decomposition of the E6 reps: E6 singularity is needed, requiring F-theory and the "5.10.10" coupling in SU(5) is generated from the E6 structure, too. Now, one can show that the 7-branes supporting the gauge fields must be del Pezzo surfaces because they must be able to shrink, giving you a positive curvature. The surface is essentially unique.

The Wilson lines can't be used to break the GUT symmetry here since the del Pezzo has no cycles. The right Higgs can't exist either because that would correspond to a non-existent deformation of the local geometry. One is forced to use the fluxes. The cycle is determined! It must be mapped to a root of E8.

Geometrically, he has to solve the doublet-triplet splitting problem and the solution automatically solves the proton decay problems, too: quartic terms in the superpotential (from 4-fold intersections) are absent. Predictions for light and heavy neutrinos seem reasonable, plus minus an order of magnitude or so. The mu-terms and SUSY breaking will follow.

The SUSY breaking is very predictive in this setup. Vafa reviews gauge and gravity mediation of SUSY breaking. The Goldstino chiral multiplet (X + theta^2 F) has the F-term. The dimension of F is squared mass. Depending on the value, one can distinguish the the types of mediation. By his philosophy, he wants gauge mediation because gravity is decoupled. But now, B mu term can't be made small if the mu-term is large enough.

So the mu-term must come from a D-term (Giudice-Masiero mechanism), like in gravity mediation. Tan beta is then naturally large, and the small bottom/top mass ratio is thus natural without fine-tuned Yukawa couplings. All scales are then fixed, close to the sweet spot SUSY, and the Peccei-Quinn 7-brane is paramount for SUSY breaking. The PQ symmetry is anomalous and Higgsed by a GS mechanism. String theory allows them a hybrid of Fayet and Polonyi models. The QCD axion arises automatically with a marginally tolerable decay constant, 10^{12} GeV. The good things, like the correct U(1)_{PQ} charges, are obtained from the E6 symmetry, without the extra field-theoretical E6 baggage.

Cumrun is finally able to make extremely accurate predictions for the LHC. The Bino is the lightest superpartner, followed by stau. Tan beta is between 20 and 30 (an unusual value, a bold prediction, indeed). A brilliant talk.

Question: is there a IIA mirror dual? Cumrun is not sure whether it exists at all. Question: how can the instantons be suppressed if you're in non-perturbative regime? Cumrun says that non-perturbative is about "tau" but the suppression is due to large volumes. Another question is answered by "F wedge H is zero".

Cumrun spends his coffee break by off-camera, on-microphone discussions, mostly with Andy Strominger. Those 6 meters in between their offices in Cambridge are probably too many so these questions haven't yet been answered. ;-)

After the coffee break, Alessandro Tomasiello continues with a talk about AdS4 flux vacua (PDF here). Some people are motivated by AdS4 as the starting point for realistic vacua. He is motivated by knowledge of some stringy geometry (theoretical motivation). He will look at AdS4 x CP3. At some point, SUSY may become N=6, an old solution whose CFT3 dual was found recently. He explains how generalized how-flat (generalized complex) manifolds are defined, by the amount of SUSY. The SU(3) structure manifolds - a subclass - is more well-known.

The wedge products still vanish, like in Calabi-Yaus, but the exterior derivatives of J, Re(Omega) don't: they're proportional to the other form. Some bad news about the vacua are mentioned. But there are many of them. ;-) So he's listing various manifolds with N=3 (and N=2, N=1) SUSY, without explaining too clearly what (how complete) the list exactly is. A double-U(1) quotient of SU(3) has a known CFT3 (quiver gauge theory) dual.

A list of allowed topologies (sometimes with several metric per topology) increases a bit when some masses are allowed. It looks somewhat disorganized to me. A moduli space is found to be a line interval but that's an inaccurate artifact of SUGRA because 1) flux quantization, 2) string corrections. Some pictures with the angle whose meaning I missed are shown. Are there many animals of this kind, he asks? Answer: a question mark.

Conclusions: even for simple topologies, there are often infinitely many vacua (with N=3 Chern-Simons CFT3 duals). Question: Michael Douglas wants to defend his statements about the finiteness of the number of vacua, so he points out that if one restricts the size of hidden dimensions, the number is finite. Answer: confirmed.

Timo Weigand talks about D-brane instantons in type II orientifolds, a technical topic that was investigated in a lot of papers during the last year (PDF here). The motivation seemed confusing. But the technicalities have content. D-brane instantons are divided into two groups - whether or not their cycles are inside existing physical D-branes. If they are, they can be interpreted as stringy realizations of gauge instantons. If they are not, they are exotic stringy instantons. A lot of work has been done and won't be mentioned.

First, he counts zero modes on the instantons. They come from open strings that can either end on the same D-brane instanton or two different ones. The first group has some universal modes; the second is typically found near intersections and has phenomenologically interesting couplings.

Superpotential can only be generated by BPS instantons, and not even all of them: two zero modes must be lifted. By picking a transverse geometry or e.g. a flux or ... by interactions in the E-E' sector. (D-terms are contributed to by non-BPS, off-calibrated instantons.) Concerning the latter, the goldstinos are lifted by this E-E' stuff. Now he, somewhat repetitively and off-topic, jumps to the other ways of lifting the zero modes.

He talks about the invariance of the instantons under the orientifold transformation. At some points in the closed-string moduli space, you're forced to choose bound states of instantons. A rather complicated discussion which terms are generated by various bound states of the instantons appears here. Chiral intersections can prevent the instanton action from having any method to lift the zero modes (global constraints, related to index theorems etc.). By looking at lines of marginal (or, later, threshold) stability, one can see that the instantons should be allowed to split etc.

He argues that only certain superpotentials can occur from the D-brane instantons: they should satisfy similar charge constraints as the perturbative terms, except that the balance may be shifted by the charges from the additional zero modes. This stuff has various applications. One of them is SUSY breaking by F-terms: production of Polonyi terms. He tries to construct a full-fledged SUSY breaking scenario. The context is somewhat unclear to me. Question/complaint: Cumrun says that the U(1) and SU(5) couplings should be naturally identified which makes it unnatural to produce the "5.10.10" coupling in Timo's way. Yes.

Stephan Stieberger titled his talk "Superstring amplitudes and implications for the LHC" (PDF here). It's focusing on tree-level multi-point amplitudes, their compact form (e.g. six-gluon disk amplitude), and possible stringy signals at the LHC relevant for QCD jets.

Now, he reviews the MHV-like QCD amplitudes (we know from the twistor industry). The next slides are about SUSY variations of vertex operators. He argues that certain recursive relations for multi-point MHV QCD amplitudes hold to all orders in alpha' in string theory (universal for all compactifications). SUSY Ward identities reduces 6-point amplitudes to simpler ones. Then he wants to get the full n-gluon amplitude in string theory from the "first principles", namely from the correct soft boson limit, collinear limit (factorization), and permutation symmetries.

He looks at various arrangements, e.g. 2 gluons and 2 chiral fermions. The results so far are universal for type I and type II theories. To see some stringy stuff of this simple kind at the LHC, he needs to assume ADD large dimensions. To see the strings, he would look at dijet events and Regge excitation resonances in the s-channel. Well, it would indeed be easy to see the strings if they existed there. Now, the discussion almost looks like Chapter 1 of the Green-Schwarz-Witten textbook. High-precision tests would tell us about the internal shape but he doesn't specify how the reverse engineering is made.

A question: what are you doing with background? Answer: Yes (not clear what he exactly means). ;-) Another question from Kiritsis: why haven't you seen the Z'-like particles at 100s of GeV that would exist for a TeV string scale? Answer: Z' are irrelevant. A small argument explodes. At any rate, I agree with the guy who asks that these models are already excluded.

Ron Donagi started the afternoon session with Heterotic Standard Models, a topic that was repeatedly covered on this blog. The talk began with a technical interlude, namely a struggle involving the screen size of the Apple's PowerPoint (or replacement). The Apple devoured his paper. It was a really good paper. A kind of a bummer. Applause. :-)

Juan Maldacena was ready to jump onto the scene and speak instead about the membrane minirevolution, namely their "ABJM" N=6 supersymmetric U(N) x U(N) Chern-Simons SCFT in three dimensions, generalizing the Bagger-Lambert-Gustavsson theory (PDF here). He wrote the action and demonstrated its classical scale invariance. Then he mentioned that N=3 CS-like (with Klebanov-Witten quartic superpotential) theories are common in 3D. He doubles the supercharges by looking at some R-symmetries.

The theory describes M2-branes proving an 8-manifold with a R8 / Z_k singularity. In detail, two NS5-branes with N D3-branes gives Yang-Mills plus bifundamental matter. One NS5-brane is rotated, we get N=3 YM CS plus bifundamental hypers. Some dualities lead to M-theory with two circles. Two KK monopoles are possible and their intersection is a special kind of hyperKähler singularity. Close to the R8/Z_k singularity, SUSY is enhanced to N=6.

1/k plays a role of the coupling constant: the theory is free for large "k". There is another parameter N, the number of M2-branes, and 't Hooft limit is possible for N/k=lambda fixed and N large. For N=2 and U(2)'s replaced by SU(2)'s, one gets the Bagger-Lambert-Gustavsson theory.

The gravity dual involves AdS4 x S7/Z_k, with a free action. For large k, Z_k "becomes" U(1) and S^7 becomes CP_3 - Tomasiello's talk... When he calculates the thermal free energy, the 3/4 from YM is replaced by 1/sqrt(lambda). He discusses operators - some BMN-like traces as well as 't Hooft operators (postulating a unit of magnetic flux around one point). A bifundamental operator must be added (k of them). The BMN-traces are simply type IIA strings, with no KK momentum along the Z_k orbifolded direction. The others are D0-branes, with a D0 momentum.

For k=1,2 he gets enhanced symmetries, analogous to SU(2)'s at the self-dual radius, in this case ordinary SU(4) and/or an extra center-of-mass symmetry for k=1. Similarly to AdS5 x S5, it seems integrable (classically) and you wonder whether it is an exact statement.

Changing U(N) x U(N) to two different ranks is like adding torsion F4 flux in M-theory. You can't find a Lagrangian that would flow to it. One can try to orientifold the theory, squash the 7-sphere, take more complex quivers, etc. So in conclusions, they have presented a surely interesting theory. He wants to master the 't Hooft operators, decide the integrability, maybe find duals of more general AdS4 vacua, and study the condensed-matter applications (which is likely for their theory than to describe the Universe).

A question why it is a gauge theory or something like that - hard to heard through the noise. Juan didn't quite know the answer. Another question: why would you expect conformal invariance? Answer: SUSY, presence of singularity in the moduli space. Third question: what condensed-matter applications? Answer - two: either 2+1-dimensional systems; or the Euclidean version may be good for critical phenomena. Another question: can you get the Yang-Mills limit (for k=1)? Answer: repeating some BL-G wisdom plus no answer about k=1.

Ron Donagi has another attempt (PDF here). Everything works now (except for the letter "B" at the end of every line). Heterotic Standard Models are the High Country of the landscape (anti-swampland): only 1 item is known right now. They're looking for full global models only. He plans to cover 7 papers, 6 of which included him, one of which is in preparation (with a female co-author).

The playing field is a Calabi-Yau with a SU(4) or SU(5) polystable bundle. Anomalies must be canceled: c2(X)-c2(V)=[M5 branes]. Commutant H in G is the low-energy group, Wilson lines (Z2 for SU(4) or, for SU(4), Z3 squared or Z6) get you to MSSM, 3 generations must exist.

For his favorite SU(5) case with Z2 Wilson lines, he needs a manifold with a freely acting Z2. Xtilde, the larger manifold, is either his favorite fiber product of two del Pezzo surfaces. Or a complete intersection of 4 quadrics in CP7. ;-) His way is the only close to MSSM so he explains the fiber product. It's like a Cartesian product of two elliptic fibrations except that you only take the points with the same location on the two fibers, effectively removing one of them. The manifold has h12, h11 equal to 19, 19, superficially a self-mirror.

Fourier-Mukai transform is used to construct the (Z2-invariant) bundle. Sometimes, monads are helpful etc. The anomaly is canceled either by M5-branes or, preferably, by bundles in the hidden sectors.

Years ago, he expected the model to be the first example among zillions. It unexpectedly remains the only one. So he still finds it ludicrous for him to successfully describe the Universe by his first algebraic geometry construction but the audience is clearly expected to be more optimistic. ;-) My estimated probability that their precise model is right is comparable to 1%. Phenomenological properties seem OK - pure MSSM, R-symmetry preserved classically (stable proton), semi-realistic Yukawa couplings and mu-terms.

There are other models which don't have stable V (Braun et al.). NAHE by Faraggi et al. are mentioned, too. Relaxing one of the conditions expands the landscape hugely. Now he talks about many not-quite-realistic models, including the (51,3) Vafa-Witten model, classified by various groups etc.: large tables with discrete data. A (2-9) free fermionic model is connected to their geometric compactification.

In the new paper, they have 1 construction that may generate a couple of new examples (or not). To summarize, the High Country is small and only has 1 fine representative right now. His plan involves strategies to look for new geometries and bundles. I think they should pay much more attention to detailed investigation of their best model. Stabilization & F-theory duals should be looked at.

In the question period, a participant claims that you can use fluxes to break the group. Another question is answered by Donagi's absent taste to study asymmetric orbifolds and nongeometric models. Another question is what they do with the hidden E8. Initially nothing. Later, it has a bundle on it. Addition to the question: he thinks that if both E8 can be used nontrivially, the High Country expands dramatically, he says. Donagi would like to know details.

Neil Lambert - now a part of Bagger-Lambert - will unsurprisingly talk about multiple M2-brane Lagrangians, the membrane minirevolution he helped to spark (his PDF is here). He can't enumerate all the work here - there has been too much. M-branes are hard, there's no dilaton to make it weakly coupled. The Lagrangian description is not known - a point to be challenged (although Juan's challenge has probably been superior by now).

For a stack of M2-branes, the SUSY variation of X is universal - schematically epsilon times psi. The variation of psi is epsilon times partial(X) plus a cubic term in X, in this case, times epsilon. So he's led to a 3-algebra (something with a triple product). Historically, he reviewed his steps to construct the Lagrangian. Click at "membrane minirevolution" above to see more comments about this construction; I won't repeat it here.

The algebra closes if the mutated Jacobi ("fundamental") identity holds. The Lagrangian eventually has the right symmetries, including parity (that was hard). The SU(2) x SU(2)-based 3-algebra, the simplest example, is explained. There are infinite-dimensional examples (equivalent to an M5-brane?). Their simple theory has R8 x R8 / D_{2k} for the two membranes. For k=1, it only differs by a O(4) vs SO(4) difference. For k=2, it works. For higher k, the orbifold action looks weird: the coordinates of branes are nontrivially mixed/rotated together as a doublet. ;-)

The origin of N^3 is hinted. Enhanced symmetry (classically) appears when the branes are collinear, not necessarily coincident. When the 4-index structure constants are non-antisymmetric, there are infinitely many examples but there are no gauge-invariant observables. The status of the non-unitary, indefinite algebras is not yet settled while "ABJM" (see Maldacena above) is where the field has gone. Various other modifications - like "ABJ" with torsion - are mentioned.

For SU(4) x U(1) smaller R-symmetry replacing SO(8), they're led to new symmetry conditions for the structure constants. They're Riemann-tensor-like symmetries, with an extra complex conjugation for the exchange of the pairs of indices. You find an infinite class of 3-algebras here, with explicit "XZ*Y - YZ*X" formulae for the 3-product. Many more papers with new groups, classifications of models etc.

To conclude, they constructed a unique (but k-labeled) theory for multiple M2-branes. The only example of a maximally supersymmetric gauge theory without gauge bosons is it. ABJM is the interesting broader class. He bets - but can't prove - that the N=8 theory is relevant for M-theory even above k=2. Can we see the 3/2-th power in the entropy? Vague proposals.

Do we really need the 3-algebras? You're right, we don't. ;-) But they have the same classification. But the physical fields, scalars and fermions, don't directly see the 3-bracket. His mother is one of 2 people who believes that something here is interesting ;-), thank you. Some questions. The first had a vague answer. The second, about coupling to SUGRA backgrounds, is also unclear. Many other questions are asked (Neil is a great person to answer questions), for example: why can you only describe 2 branes? Neil thinks that it just seems to be the only number for which this theory works (some special features of the orbifold).

To make the topics diverse, Sunil Mukhi - who is also a blogger ;-) and who is blogging from the coolest place in the Universe - speaks about the membrane minirevolution, too (PDF here). He will try to minimize the overlaps. He will describe roughly 3 papers, including the D2-branes from M2-branes that we reported at the beginning of the minirevolution.

Sunil is funny. There was an agreement that it (M2-brane Lagrangian) couldn't be done because it was not done. But now, once it's been done, we agree it can be done but it should be done better. In France, they have "brane" wines - a bottle shown on a picture. ;-)

His interest is in the extension of SO(7) to SO(8) and his classification of the known algebras is from a somewhat different angle. Unlike other speakers, he finds the indefinite 3-algebras interesting and he will focus on them. A new gauge symmetry manifestly removes the bad ghosts (and some good things, too). Some overlap with "ABJM" and "ABJ" is mentioned. New excuses why the theory is not known for N above 2: it would be strongly coupled, anyway (and the classical Lagrangian not overly useful).

As explained in the "D2 from M2" article linked above, Sunil tells us how the gauge field becomes dynamical - a new kind of Higgs mechanism. How is it possible that Higgsing makes a compactification? Because of higher corrections in 1/vev. The decoupling is only for infinite vev (like in our deconstruction paper with Nima et al. that Sunil mentions: yes, the derivation of the cylinder limit from the cone, and the stringy duality derivation from the quiver, was my work in the paper). In this present setup, the large vev can be replaced by a high level (order of the orbifolding group).

Finally, something that Sunil found pretty, then ugly, and now again pretty. ;-) The Lorentzian algebras. He adds some B-wedge-F terms to the Lagrangian. These theories violate Juan's wisdom that one can make a theory classical by adding a large classical prefactor to the action: if you add one, you can get rid of it by a field redefinition. The Higgs mechanism works in their picture but it works too well. ;-) More precisely, one gets the exact Yang-Mills (a reformulation? that seems disappointing).

To show the equivalence, non-Abelian dNS symmetry produces a non-dynamical gauge field: harmless. The duality works, by integrating out something (B?), and he explicitly constructs a Lagrangian where the SO(8) symmetry emerges except that it should also act on the coupling constants. To summarize, after some exercises, one can rewrite the N=8 Yang-Mills in a (Lorentzian) 3-algebra friendly way. But the superconformal and SO(8) symmetry is broken immediately when the vevs etc. are added.

Last two minutes dedicated to extra topics about the Lorentzian algebras: can one generalize the steps above with alpha' corrections added? Will the 3-algebra structure survive the stringy additions? So he adds a lot of F^4 terms and those of the same order. After the procedure, the result is still SO(8)-invariant! The enhancement works to all orders. To conclude, there's been much progress for multiple M2-branes but not a complete progress. A funny picture at the end.

For the third talk about the same topic, it was an extremely refreshing and original talk! ;-) Question: is the equivalence classical or quantum? Answer: it was done classically. Juan: what's the Goldstone boson for the broken conformal symmetry? It's not there - the field must be constant. New question: make D2-branes in a varying dilaton. Will the X8 vary? Sunil sees no problems but warns that the variations of other fields can't be forgotten.

Tuesday talks are over. The text above is too long, too few people will read it, and I won't be fixing the typos, sorry.

Monday, Tuesday, Wednesday, Thursday, Friday

Strings 2008: Monday

...and live broadcast



Click the picture above for the Strings 2008 website. Click here for a separate window with the live webcast.



On September 10th, the video above also broadcasts the live webcast, "The First Large Hadron Collider beam", since 9:00 am Prague=CERN Summer Time (midnight Californian daylight saving time).

Monday morning

At Strings 2008, some officials gave nice introductions in the morning. It was announced that 1 octant of the LHC is already testing a beam (probably 81 whose chart says "hot" now: everything is at 1.9 K, however). String theory was also presented as a tool to achieve peace - which was also the reason why they established CERN itself. ;-) Funny.

Gabriele Veneziano spoke about high-energy string scattering that played an important role when he initiated string theory (at CERN) exactly 40 years ago. However, he focused on some newer work on the scalings. Although I view these topics interesting, I found the talk a bit boring, full of too many "small points", and I think it is wrong that the discipline and time schedule was not demanded by the organizers.

Andy Strominger was caught in a cute debate about e-mail with a female colleague before he began his talk. ;-) In 2 seconds, he - a Windows guy - learned to walk forward and backward (with a Mac). He prepared a talk about chiral 3D gravity that we have discussed two weeks ago.

He nicely motivated his talk by saying that string theory is the only consistent quantum framework complex enough to contain black holes but it would be better to have simpler toy models for some purposes. He said that 3D gravity may look trivial (Einstein's equation = flatness) but it actually had (BTZ in AdS) black holes so there could be something. But is there a full theory?

Andy was implicitly skeptical about Witten's monstrous work and added the chiral term and explained physics of the theory, carefully looking at the asymptotic isometry group - the quotient of the allowed and trivial diffeomorphisms. The theory becomes chiral at the critical vacuum energy. The holomorphic factorization, assumed (but probably incorrect) in Witten's monstrous case, becomes a consistency requirement.

Finally, he connected the work with observations - namely those of extremal 4D Kerr black holes: everything must move counter-clockwise around the horizon which is analogous to the chirality in the 3D case. He manages to properly reproduce the "S=2.pi.J" entropy of these black holes. He finally conjectures that a black hole in the telescope is dual to a c=2e46 CFT or something like that. Excellent talk!

Jeff asked about monster symmetry of Andy's CFT. Andy interpreted Davide's paper as making it impossible to have monster symmetry reps above the k=1 level. But in 4D, the monster group could be there.

Renata Kallosh updated her 2007 talk on string cosmology. She began with the WMAP5 successes and with the proposed stringy models of inflation with gravity waves. LambdaCDM is not going to go away: physicists should "adapt" to it. ;-) She advocated the landscape description of these things and encouraged people to develop "as many models as possible" so that they can fit the future data - a formulation I find amusing: if you cover a parameter space by models, it doesn't mean that the model that happens to coincide with the observed parameter is the right model (a truism that the anthropic people could disagree with).

The B-modes could be observed soon (or the bound moved by a lot), she says. A racetrack model of hers predicts no cosmic strings and no gravity waves. Silverstein's work deriving gravity waves from monodromies was described. There's been a lot of experimental charts in the data. 10% of cosmic strings with n=1 (exactly) works as well as 0% of cosmic strings with n<1.

She described a general problem of their favorite models predicting observable gravity waves: natural models typically predict very heavy gravitinos, with masses above the inflationary Hubble scale. My conclusion would be, of course, that it is fair to say that they predict that gravity waves won't be seen.

That ends the main part of her talk. But she mentioned a few words about her involvement in the finiteness of N=8 supergravity. She will publish a preprint tomorrow about this idea. Her proposal is to link the counterterms in the 4+32 covariant superspace with those in the 4+16 light-cone superspace, using the helicity variables. She claims that she has proved the perturbative finiteness (the counterterms would break Lorentz symmetry in the light cone gauge) assuming the absence of BRST anomalies in N=8 SUGRA (i.e. that it's possible to express N=8 SUGRA, whatever it is, both covariantly and in the light cone gauge equivalently). Very interesting.

Alexander Polyakov, the father of many things including the Polyakov action, prepared a talk on global warming. ;-) Well, global warming of de Sitter space. The global warming fad has gotten very far: a string theory conference. The talk began with a global dimming of the video. He continued with tired mountaineers :-) and after 5 minutes, I have still no idea what the talk will be about. After 6 minutes, he finally mentioned an interesting question I care about - how does highly-curved AdS/CFT gravity becomes a free gauge theory. But he won't be talking about it.

Instead, the talk is about the de Sitter space but I still don't know what exactly it will be about. Something about particle production in it. But what? Fine, after 15 minutes, he said he wants to refine the Bunch-Davies propagator. He requires the eternity condition (in-vacuum = out-vacuum). Spider (pure creation) diagrams vanish (no particle production proving instability). After 20 minutes, he said he is just beginning his talk. ;-)

He asked whether this stability (cancellation) is possible in other FRW geometries. Has it something to do with the Huygens principle (different in even and odd D's)? I don't know. ;-) At this moment, it's clear that the talk is about the de Sitter stability. The title is explained by a nonzero probability for the temperature to grow at each point of de Sitter space. I missed where it came from. 2 minutes after the normal end of the talk, Polyakov was talking about two squirrels watching a gymnast. ;-) Great Gentleman, very chaotic talk.

Hirosi Ooguri asked how he wants to analytically continue the coupling and adjust it at the same moment. I didn't understand the answer. Andy Strominger asked something and the answer was not known. Juan Maldacena asked in which formalism the Bunch-Davies vacuum was claimed to be unstable. I think that Polyakov avoided the direct answer but he probably thinks that it is unstable in all approaches.

Monday afternoon

This half-day is dedicated to talks about the LHC, the collider scheduled to run a mere 500 meters (ATLAS) from the conference hall (Main Auditorium) on September 10th.

Lyn Evans, CERN's manager, begins with a description of the status of the LHC machine. Casually dressed, he announced all the octants to be at 1.9 K - even though the picture shows a hot 81 sector now (because of a beam?). Geography of the sectors - mostly independent "factories" - is explained. There's a lot of pre-acceleration. The LEP infrastructure was re-used to reduce the price of the LHC by 50%.

The 1.9 K temperature is below the cosmic microwave background and it is the coldest place in the Universe unless some aliens are ahead of us in particle physics. ;-) Funny music begins to play. String theorists are then explained how to create a perfect dipole field (Rob Myers doesn't have to listen now). 1.9 K was chosen for the helium to be as heat-conductive as possible. A non-trivial transition from 1.9 K to 4 K is needed: superconductors can't support temperature gradients. High-Tc superconductors are helpful.

Cooling and warming is fast enough now for a problem to cost 3 months of interruption. He showed and explained the temperature charts of the sectors. Now, when the sectors are cool, they are commissioning the hardware. Hundreds of circuits and 1,600 power supplies must be tested individually. Global tests of arcs will follow. Beam commissioning worked instantly on 8/08/08, when the Olympics and the South Ossetia war began. Champagne. Things look great, many inverse femtobarns will be collected in 2009.

Question: What is training of magnets? Another question: PS (Proton Synchrotron, *1959) is the oldest thing and it will collapse, like all old things, what will you do? Evans: It works well but in a few years, it may be renovated.

Jos Engelen spoke about detectors that are also ready. They have to sustain higher energies, luminosities, and speed than their ancestors. Size is increased. Every 25 nanoseconds, there's a beam (in fact, with 1,000 tracks) hitting you. Fast materials and many pixels are needed. Like the rapping Alpinekat, he explains what LHCb, ALICE, ATLAS, and CMS will be doing. Also, TOTEM will look at the total cross section, LHCf for something else, and a place will look for magnetic monopoles.

He talks about the resolution of muon energy and missing transverse energy. The detectors should be affordable, he thought when he was young. ;-) Multiple scattering has to be avoided (light thin material). No cracks! Muon spectrometers work differently at CMS and ATLAS (the biggest difference between the two) - tracking mostly inside or outside, respectively. A lot of details about calorimetry etc. It's impressive but overwhelming. ATLAS is a ship in the bottle. ;-) The LHC is not quite horizontal: extra mechanical support for the detector is needed. CMS is more compact than ATLAS (that's the "C") but modular.

In 2008, CMS and friends are ready for the 10 inverse picobarns and to re-discover the Standard Model. ;-) ALICE will track heavy ions - lower luminosity, higher multiplicity. Some of the detectors are not in the full 4.pi directions. In LHCb, everything is just 1/2 of a full detector, for money reasons. The grid is a reality, 100,000 processors will deal with 15 terabytes a year. The Higgs and SUSY may come in 2009. Question about upgrades: multiplying the luminosity by 10 will require new detector centers. Question about energy upgrades: up to 10% can work for free. Question: what was the best and worst decision? The best was that Lyn became the boss and the worst decision - he can now answer what it is. ;-) Question: whose triggers are better? They're different. ATLAS used classical, level 1,2,3 triggers while CMS chose a technology that didn't yet exist at the time.

Oliver Buchmüller talks about new physics at the LHC. His talk has three parts: the challenging LHC environment; the Standard Model rediscovery; and CMS and ATLAS scenarios to see new particles. Hard environment: new high energy makes old things look new, cross sections can be very low and very high. He already showed ready abstracts of papers announcing discoveries of new charged particles at sqrt(s)=10 TeV. ;-)

But in 2008, they must start with rediscovering of the Standard Model (maybe including the top quark), a pillar for new discoveries. When will those occur? Either early or late, the historical data show. ;-) The light Higgs (115-120 GeV), favored by Tevatron, will take a long time to be discovered. Peskin said that once the Higgs will be seen, it will no longer be interesting (because other new physics will already have been found). LHC may become a huge SUSY factory quickly - by 2009 - but only if the detector behavior and backgrounds are well understood.

He explained a point misunderstood by some theorists. "SUSY search" doesn't mean that they're dogmatically believing a particular theoretical model. It means a class of events - signatures - in this case a lot of missing energy plus a lot of leptons (from a cascade decay of a heavy new particle): so the "SUSY search" can stand for many other types of models, too. Also, the Higgs is wanted, dead or alive. Bounty: USD 5,000 and probably USD 10 billion because finding it is enough to make the LHC worth it, he thinks. For the mass below 200 GeV, the peak is very small and we may wait until 2010-2011. Exotic new physics at 1-3 TeV sometimes...

Question on black holes: they could be seen in 2009 if they exist. Question: smoking gun for SUSY (and not something else)? Hard to determine the spins directly etc.

The talks from other days are available in separate articles:

Tuesday, Wednesday, Thursday, Friday

Climate debate: realist Monckton beats alarmist Littlemore

Start with the bottom part (1/4) to listen to this radio debate on climate change. A podcast page dedicated to the event is available, too. The debate is a full-fledged war, starting with discussions of Littlemore's blog's financial connections to organized crime.

But Roy Green, the moderator, makes it sure that they return to the climate issues (the hockey stick graph, Bangladesh, warming on other planets etc.) soon.

As expected, Christopher Monckton who is not only a skeptic but who has become quite a complete climatologist defeated Richard Littlemore, a climate alarmist who has really no idea about the issues, rather easily.

Lord Monckton joined many other skeptics who have won over alarmists in the past, including the victorious Crichton-Lindzen-Stott team (against Schmidt et al.), Joe Kernen (against celebrities), Richard Lindzen (against Bill Nye), skeptics at TalkClimateChange forums, and many others. Congratulations!

Related: Tara Brown (pic) fairly and sensibly interviewed Kevin Rudd on climate change on the "60 minutes" show

Green activists at DeSmogBlog were impressed by Lord Monckton's performance:

Unfortunately... at the moment it seems Littlemore's being led around by Green and Monckton. Take back control! Take back control!

I'd have to say that Monckton "won" the debate. He came across as more prepared and had answers at his fingertips, whereas Richard appeared to verbally stumble on occasion...

Richard Littlemore admitted defeat here:

In hindsight, I played perfectly into the hands of Monckton and his happy radio host, Roy Green, who share the same goal... Score one for Monckton.

Another pro-Littlemore website thinks that Littlemore was completely unprepared, too.

I don't think it's really possible for alarmists to win a debate because their position doesn't hold much water.

If they want to succeed, they must build on human ignorance, fear, censorship, intimidation, ad hominem insults, and oversimplified slogans. Any format where nontrivial scientific facts and ideas can actually be presented and discussed is bound to be a failure for the alarmist movement.

Hat tip: Liberty News Central

LHC: panoramic pictures

Peter McCready has combined 102 high-resolution photographs of the LHC collider and its detectors into 12 amazing virtual-reality, full four-pi-steradian simulations that include some authentic sound. You can drag and move the picture and hear the natural sound, too! Flash is needed.

• *901.html ATLAS commissioning 1
  
• *902.html ATLAS commissioning 2
• *903.html Cryogenic dist. line commis.
• *601.html CMS commissioning cavern 1
• *602.html CMS commissioning cavern 2
  
• *603.html CMS commissioning hall
• *604.html CMS outside
• *605.html CMS strip tracker commis.
• *606.html ALICE commissioning
  
• *607.html ALICE beryllium beam pipe
  
• *608.html Sector 8-1 commissioning
  
• *609.html Magnet interconnections
  

The complexity and the very size of this gadget - or 27 kilometers of heavy industry - may look crazy and it was rather expensive, too, especially if you realize that its only purpose is to subtly help a few hundred people similar to your humble correspondent to decide which string theory scenario is more likely. ;-)

On the other hand, the money needed to pay for the whole LHC collider is lost in the gray economy of carbon indulgences every week! People could indeed do amazing things if they wanted and if they didn't allow idiots to manipulate with others.

Via Symmetry magazine (*), Nude Socialist (*), and iSGTW (*).

Dozens of exciting articles about the Large Hadron Collider may be found e.g. in the LHC category.

Koutsoyiannis vs RealClimate.ORG

In this dose of peer-reviewed skeptical literature about the climate, we look to the Hydrological Science Journal. D. Koutsoyiannis, A. Efstratiadis, N. Mamassis, and A. Christofides wrote a text

On the credibility of climate predictions (PDF).

They simply compared the local predictions for temperature and precipitation by many models with the real observations and found out that:

... The results show that models perform poorly, even at a climatic (30-year) scale. Thus local model projections cannot be credible, whereas a common argument that models can perform better at larger spatial scales is unsupported.

Gavin Schmidt decided to criticize paper:

RealClimate.ORG

If he has an argument against the paper, I haven't found it. I agree with Schmidt's comment that it should have been expected that the models won't reproduce the local climate - even though our expectations could have very different reasons (my reason is that I simply know that the existing climate models don't properly deal with most of the essential climatological processes; I am not sure about Gavin's reasons).

But Koutsoyiannis et al. probably agree with it, too. (Confirmed by the lead author himself in the fast comments.) However, Koutsoyiannis et al. say not only that the local predictions of the models have been falsified: they also correctly say that the statement that the predictions would work at the longer distance scales is unsupported. And it is unsupported, indeed.

What does the word "climate" mean? It is the information about the behavior of the weather in a given region at time scales longer than 30 years or so. When we talk about the climate, we may be averaging over longer time scales but we are surely not averaging over the planet. Climate is always associated with a region: that's why we can distinguish tropical, dry, moderate, continental, and polar climates. ;-)

There is no "global climate". When people talk about "global climate change", it is the whole "climate change" that is supposed to be supplemented by the adjective "global": we are surely not talking about the changes of the "global climate" because the latter doesn't exist. Even Wikipedia controlled by William Connolley seems to agree with this proposition. It is strange that Gavin Schmidt seems to disagree.

So the short-term weather signals are averaged out but as Koutsoyiannis et al. show, it is still not enough to obtain an agreement between the models and the reality. The models clearly don't reproduce many changes well, especially not the changes driven by the long term persistence (or auto-correlation) of the time series. Note that the Hurst exponents determine the "color of the noise" and because these exponents generically exceed 0.5 in climatology, the long term persistence (the "inertia" of the climate) is very important.

Even if you don't understand these words about the Hurst exponents, you should understand that the predictions of the climate models for any particular region in the world will be essentially uncorrelated with reality because the reality is dominated by effects that are not properly simulated by the models. Because every single person lives in a particular region of the world and every region of the world is more or less incorrectly predicted by the models, I think it means that no rationally thinking person should pay serious attention to the predictions of these models.

And can the models become good at long distance scales again? Maybe. But it is extremely unlikely. If you think that they do become good at the global scale, you are believing in a very contrived, fine-tuned hypothesis: all the detailed (short-term, local) data that can be tested come out incorrectly but only when you care about one number - the global long-term temperature trend - all the errors must conspire and evaporate.

So the fashionable "climate change theory" is supposed to be an effective theory that only works at distance scales T and length scales L that are longer than certain bounds. If you want to believe that Gavin Schmidt is right, you must also believe that T must be between 30 years and 100 years and L must be greater than 6,000 km or so but shorter than 40,000 km. Why? Because the theory is falsified by the observations at shorter time and distance scales (the detailed local and/or meteorological data). But for the theory to be relevant for the Earth, the distance cutoff must be shorter than 40,000 km. And for the theory to be scary enough for a few future generations, the time cutoff must be shorter than 100 years. ;-)

When you average the known data over these very long scales, you are exactly at the moment when you lose all nontrivial climate information that could have been used to validate the model. It is exactly the moment when you are supposed to start to believe the models.

I find such a belief unjustifiable and crazy. If an effective field theory only works well enough at distances longer than a cutoff scale L, there is absolutely no a priori good reason why L should be between 6,000 kilometers and 40,000 kilometers! ;-) 1,000 km is already a very long distance not only for a particle physicist :-) but also for various local atmospheric variations to average out and for a useful approximate theory of the climate to start to be relevant. However, these theories seem to break down, even in their long-term predictions. When they break down at the distance scale of 1,000 km, is sounds extremely reasonable to me to assume that they probably break at the 6,000 km scale, too.

Similarly, if a theory highly incorrectly predicts the global climate trends for 10 or 20 years, which we already know to be the case from observations (even for the global mean temperature), it seems unreasonable to expect that the theory will be very accurate for 30-year, 50-year, or 100-year predictions.

Assuming otherwise is remotely analogous to the belief that Jesus Christ was the only person who could have walked on water. It may have been true that Jesus Christ was the only person for whom some unlikely cancellations of the gravitational force took place but it doesn't seem too likely to a scientifically trained ear. OK, Christian readers are supposed to hold their belief at this point but I just think that this particular belief is not natural from a scientific vantage point.

So I prefer the common sense approach of old-fashioned science: if all the detailed predictions of the existing models have been shown incorrect, it probably means that the models themselves are incorrect or at least substantially incomplete.

And that's the memo.

The oxygen crisis

Most mainstream media have abandoned almost all quality control in their science reporting that is now arguably slightly below the image of science as presented in the leading pornographic magazines.

The latest extreme example of this observation comes from a Gentleman called Peter Tatchell, a political campaigner from the left wing of the Green party (a description that probably makes Karl Marx a staunch conservative in comparison; he's been also denounced by the British Parliament as a "homosexual terrorist" in 1994):

The Guardian, China Daily

He argues that there exists a more serious crisis than the "CO2 crisis": the oxygen levels are dropping and the human activity has decreased them by 1/3 or 1/2, he says. Wow. ;-)

The reality is, of course, that the oxygen percentage in the atmosphere has been 20.94 or 20.95 percent for thousands of years and probably much longer than that (see the historical graph on page 2 of Dudley 1998 that covers 600 million years). The amount of oxygen in the atmosphere is so huge that the biosphere (and fossil fuels which used to belong to the biosphere as well) is completely unable to change this amount significantly.

It may be useful to mention that the oxygen is only 1/5 of the atmosphere and the atmosphere is just 1/1,200,000 of the mass of the Earth. However, the Earth is damn heavy, 6 x 10^{24} kilograms, so the mass of the oxygen in the atmosphere is something like 10^{18} kilograms - about 150,000 tons per capita. Be sure that we can't burn that much oxygen even if everyone in the world were using a private jet on a daily basis. ;-) There is a simpler way to see that man-made changes to the oxygen levels are trivial and we will look at it now.

Estimating the oxygen change

For a schoolboy who is not skipping his science classes at the elementary school, it shouldn't be difficult to see why we can't significantly influence the amount of oxygen in the atmosphere.

How can he do it? Well, he must realize that virtually all processes related to life and human activity - breathing (by animals and plants) and burning (combustion) - exchange the atmospheric O2 molecules by CO2 molecules or vice versa. Sometimes, one needs two O2 molecules and only produces one CO2 molecule but this subtlety won't change our final result significantly.

Virtually all other compounds participating in the relevant chemical reactions are either liquids or solids which is why they don't influence the composition of the atmosphere and we will ignore them.

When you realize what the words above mean, you will see that the man-made decrease of oxygen (O2) is controlled by the increase of carbon dioxide: they're inseparably linked to one another. The human activity has increased the CO2 concentration from 280 ppm two centuries ago to 385 ppm today (the schoolboy should have seen these elementary numbers during his "CO2 crisis" classes). Because many people don't know what the acronym ppm (parts per million) really means, even if they like to use it, let me tell you that it is the same thing as 0.0001%.

So the carbon dioxide went from 0.028% to 0.038%: the difference is 0.01% of the volume of the atmosphere. Because O2 and CO2 molecules occupy the same volume at a given pressure and a given temperature (since pV = NkT), the decrease of O2 should be equal to the increase of CO2 if the molecules were exchanged for one another: the oxygen should drop by 0.01% of the volume of the atmosphere.

As we have already mentioned, two oxygen molecules are replaced in typical "combustion" chemical reactions for one carbon dioxide molecule, so the oxygen drop might be 0.02% instead of 0.01%. However, in the long run, there exist other processes besides the combustion-like processes involving CO2 that we have considered - for example processes involving deep ocean sediments - and these processes tend to restore the oxygen levels (as well as the CO2 levels).

At any rate, you see that the oxygen level couldn't have decreased by more than 0.01% or so, from 20.95% to 20.94%, which is pretty much exactly what was observed. We needed centuries or millenia to achieve this modest "goal". It is very clear that even if we burned all forests, plants, animals, and fossil fuels in the world, we couldn't get the oxygen levels below 20% (and maybe not even 20.9%).

Evaluating the impact

Does the tiny decrease of oxygen levels change some important things? It doesn't. The most "spectacular" change is that the wildfire risk decreases by something like 0.01%, too (and maybe slightly more), as the oxygen levels drop. Because wildfires are somewhat unpopular and their decrease would be good news, you won't read about it. ;-)

At any rate, all these changes are negligible given the tiny change of the O2 levels.

Tatchell writes "I am not a scientist, but this seems a reasonable concern." It seems reasonable to whom? To me, worries about the "oxygen crisis" seems to be a ticket for someone to be stored in a mental asylum. The point here is not whether Tatchell is a scientist: he's clearly not. The question is whether he is dangerous enough a weirdo to be isolated from the society.

We won't be able to change the oxygen level in any significant way. Incidentally, while the overall amount of oxygen in the atmosphere is essentially constant, the amount of oxygen in various parts of organisms varies dramatically. For example, the human body must keep the concentration of this harmful-if-abundant gas around 5% in most organs. Oxygen is not only a corrosive gas but also a metabolic poison under most cellular reactions. Its optimal percentage depends on the life forms which is why the varying percentage of oxygen in amber - a point mentioned by Tatchell - says absolutely nothing about the overall O2 volume.

Men have been able to change the overall carbon dioxide (CO2) concentrations measurably because it is a trace gas: there was almost none to start with, so it is easy to change its volume by relatively large amounts, proportionally speaking. But oxygen is one of the gases that the Earth's atmosphere has been made out of for 0.5 or even 2.5 billion years. You can't change that.

Incidentally, if you care how the oxygen became so important, probably 500 million years ago, the Earth needed an intense period of upheavals in its crust and it still took about 2 million years for all the change to materialize: see Science Daily. This rate is very fast from a geologist's viewpoint but surely not fast enough to be considered an urgent problem for policymakers. ;-)

Other errors

Tatchell writes a lot of other incredible nonsense, for example that the oxygen in cities is much (by 15%?) lower than it is in the countryside. He probably believes that the pressure drops from 1000 to 900 millibars in the cities. ;-) He also tries to pretend that some scientists support his idiotic propositions. Gimpy, who respects Tatchell's courage, explains that Tatchell has all the symptoms that define a crank. He satisfies most of my defining criteria of crackpots, too.

Is someone at the Guardian who has some common sense left? Could you please stop printing insane people like Peter Tatchell who help to transform your daily into an expensive and dirty piece of toilet paper?

Greenhouse paramilitia recommended to Australia

The director of the Australian Strategic Policy Institute, a government-funded think tank (or, more precisely, a place where all thinking tanks), and his collaborator have recommended new greenhouse brownshirts to protect Australia and the world:

Greenhouse cops needed on planetary beat

These paramilitary units, originally proposed by Tim Flannery as the global carbon regulating military junta, are required to "manage carbon markets" and these "will require compliance and enforcement".

It seems that the mad cow disease has been just transmitted to humans in Australia and the new mutated version of the disease should better be treated analogously to the original mad cow disease before it's too late. I really hope that the existing epidemiological methods and institutions and the existing police is enough to do the job.

Incidentally, some of the new cops' competencies are supposed to deal with the fraud in the market with carbon indulgences. That's surely a nice goal but we must ask: Much like in the case of the markets with human flesh, wouldn't it be a more sensible approach to start with banning these black markets?

Sweet SUSY from F-theory

The annual conference begins on Sunday (click).

In my opinion, the best hep-th paper this week was

Marsano, Saulina, Schafer-Nameki: Gauge mediation in F-theory GUT models

Even the PC people should be happy about the paper because most authors are female. ;-) (Well, except that the PC folks also dislike Russians like NS or conservatives like JM, but let me already stop here.)

They find out that the recent F-theory picture by Beasley, Heckman, Vafa (I, II) naturally realizes the "ultimate compromise" scenario for supersymmetry breaking, the sweet spot supersymmetry breaking by Ibe and Kitano (phenomenologists who may have actually predicted a real consequence of physics i.e. string theory!) that we discussed in 2007.

In this model, all dimensionless couplings are of order one while a scale, X, is around 10^{12} GeV and is claimed to be instanton-generated in the F-theory picture as explained by another paper from this week. The gravitino mass is around 1 GeV and dozens of canonical problems such as the mu-problem are solved (or marginally solved, if you want to be more skeptical).



IQ test: where do you think the sweet spot is on the picture?

F-theory is a natural picture where you would expect dimensionless parameters to be fully determined by known dynamics (the string coupling is geometrized and its self-dual value, around one, is special because of S-duality that is manifest) and this paper is an example of this principle at work.

Be sure that right now, because of the latest experimental data, I consider SUSY's existence to be "somewhat more likely than not" and the sweet spot is a rather natural place at the heart of the SUSY-breaking parameter space. So if I had to make a bet not only about the presence of SUSY ;-) but also about the gravitino mass, I would bet something close to 1 GeV, indeed. For the same (and related) reasons, I consider split SUSY breaking highly contrived.

Commercial break: Susskind on C-SPAN 2: four times

This may be an exciting development and all SUSY theorists should look at the papers, learn some extra phenomenology and/or F(ather)-theory that are needed in this "interdisciplinary" enterprise, and arrive at their own conclusions. I call this research direction "interdisciplinary" because F-theorists have traditionally been among the most mathematically and abstractly oriented string theorists while SUSY breaking is one of the dirtiest subdisciplines of particle phenomenology.

If the work is correct, SUSY breaking is not as dirty as we previously thought while F-theory is not as detached from the hard collider data as we used to think, either. Susie may love her sweet spot, much like jam-addicts Linda and Maleika do, as Natalia and Sakura say (sorry, Joe, there was no room for you here!). ;-)

Spurious three-loop diagrams

Sean Carroll et al. wrote a paper - see Cosmic Variance - whose main point is to superimpose several graphs indicating the allowed strength of two particular types of dark matter interaction.

Well, my general feeling about this type of phenomenology is that the amount of work needed to draw similar conclusions is so low and the uncertainty about the relevance of different types of dark matter particles and interactions is so high that it would be a better policy not to talk about similar speculative effects in detail until there is some actual evidence - observational or theoretical - that dark matter should "work" in one way or another.

A vast majority of similar papers will be proven strictly worthless by new experiments. Sometimes it's like writing papers "10^6 should probably be greater than 10", "it should probably be greater than 20, too", "and maybe it's smaller than 20 in which case it is spectacular", and so forth. Isn't it better to calculate or measure how much 10^6 actually is?

The amount of "coolness" or "importance" of such results seems to be a strictly decreasing function of their likelihood which makes me ask "What's the point?". And even if some phenomenologists study models that turn out to be (partly) valid, it can be seen that they were just lucky. Moreover, their paper won't become really "impressive" even if the model is validated because the amount of both hard reasoning and far-reaching qualitative consequences was low regardless of the validity of the model.

Shouldn't we try to quantify new effects only when there are at least qualitative reasons to consider them in the first place?



But Sean also says something about the theoretical background of their work - something that reveals his amusing misunderstanding of the meaning of 1PI (one-particle-irreducible) graphs in quantum field theory. More concretely, he claims that it is hard for dark matter to influence the interactions between a new (non-Higgs) scalar field and fermionic matter of the Standard Model.

To clarify his opinion, he draws the three-loop diagram above, claiming that it is the first diagram that contributes. You probably don't care about dark-matter contributions to some particular not-the-most-natural interactions of leptons and quarks with some new scalar fields that are not yet observed (or even substantiated) themselves but imagine that you do. How complicated diagram you have to draw?

Why is this question emotionally loaded? Well, Feynman designed his Feynman diagrams that can be arbitrarily complicated. But in reality, only the simple ones are really important in most cases. Complicated diagrams with many loops correspond to small corrections and there's not much reason to talk about them if there exist larger terms: the larger terms i.e. the simple diagrams decide about the qualitative behavior.

The simple diagrams are also much simpler to calculate which are two main reasons why most particle physicists have never fully calculated any 3-loop diagram or higher and the percentage is close to 50% for 2-loop diagrams. The convoluted diagrams are suppressed by powers of a small number "g" and the number of people who calculate them is suppressed in a similar way. ;-)

Whenever someone claims that an effect only occurs at the L-loop level (and not a lower level), it is always an intriguing claim because it suggests that an unexpected cancellation takes place. It shows that one actually has to do some abstract math - more abstract than previously thought - to understand an effect, even qualitatively. But is it true that it only occurs at the L-loop level?

In this particular case, you need the "chi" (dark particle) blue loop at the top - by assumption: you study dark matter contributions. You also need the other blue loop surrounded by the "W_0" propagators because the dark matter only interacts with the conventional matter through the electroweak interactions. You also need the "H" tadpole (the vertical propagator ending nowhere) to switch the chirality of the horizontal fermion because Sean et al. also want to study a very special type of terms here, the left-right interactions only. Note that there are so many propagators here only because Sean et al. chose to ask a very contrived and probably not too important question.

But do they need the third loop, enclosed by the "G,B" propagator? Sean says:

...But you can’t have the Higgs insertion sitting all by its lonesome on an external leg, or you don’t get a one-particle irreducible diagram. So you need one other gauge loop, either SU(2) or color SU(3), connecting the left-handed and right-handed fermions around the Higgs...

This reasoning is, however, incorrect. Where is the mistake exactly located? Well, the mistake is in the word "So" that I wrote in bold face. ;-) If a simple diagram fails to be 1PI, it actually doesn't mean that you need a more complicated diagram!

A one-particle irreducible (1PI) diagram is a diagram that "holds together" in the following sense: you can't possibly split it into two parts by cutting one internal line according to your choice. This concept is very useful because the full physical result can be written as the sum of the 1PI diagrams and other, non-1PI diagrams that can be written as conglomerates of 1PI diagrams.

But the point here is that the 1PI diagrams are useful: they are "elementary letters", in a sense. Sean thinks that they are the only ones that appear in the physical answer which is just wrong. So the correct minimal diagrams contributing to the quantity he wants is not the 3-loop diagram above but the simpler 2-loop diagram where the "G,B" wiggly line at the bottom of the picture is erased. Yes, this diagram is not 1PI but it still contributes to the physical result. Indeed, this contribution factorizes in a way but if something factorizes, it doesn't mean that it doesn't exist.

So you need two loops, not three loops, to get the desired interaction. One is needed because you want to study dark matter loops ;-) and the other is needed because you assume that the dark matter only interacts via the electroweak interactions. In other words, you get exactly as many loops as you expect. There is no surprise or an interesting result going on here and whoever claims otherwise is only emitting a nonsensical bubble of hot air.

And that's the memo.

Update: In newer comments, Sean claims that the 2-loop diagram should be excluded because it is a fermion self-energy. Well, the whole diagram (with the chi-loop) is surely not a self-energy graph. The Higgs subdiagram is a self-energy graph (well, it is really the classical mass graph in the 2-component formalism) but the whole diagram still contributes to the phi-psiL-psiR coupling.

You might want to look at the contributions to the phi-psiL-psiR coupling that are inherently different, not proportional to contributions to the phi-psiL-psiL coupling and then the differences would require you to start at the 3-loop graphs, indeed. But that's not the task that Sean outlined, so his answers to his problem are wrong. At any rate, there is no surprising or anomalously high number of loops anywhere here.

Tabarka, Tunisia & Pilsen, Czechia

Your humble correspondent is back from Tabarka, Tunisia. What a beautiful place and weather. The sea was clean, the sky was blue, the sunscreen was badly needed on the beaches, and the temperature was 25 °C higher than what we got after we returned to a cloudy Central Europe.

While AGW hysterics like an Oliver Nutcase Tickell claim that "the idea that we could adapt to a 4 °C rise [in a few centuries] is absurd and dangerous", the Czechs not only manage to adapt to a 25 °C rise in a few hours and they enjoy it but they also pay non-trivial money for such six-times-lethal excursions. ;-)

There are thousands of Czech tourists over there at every moment of time, including at least two hotels that are entirely "Czech", with the Czech language being the 4th most important language after Arabic, French, and Italian. Too bad we haven't been a colonial power so far.

English is only powerful with important jobs such as the receptionists etc. but there's a lot of international brands written in English around. You shouldn't imagine that such countries are loaded with zealous terrorists. ;-) The economical system in Tunisia is a third-way mixture led by Ben Ali, a socialist dictator.

Because of reasons I consider confidential, we also had an authentic lunch in "our" Arab family in a nearby village.

Zuzana Norisová: Pátá

Original: Petula Clark: Downtown, 1964
(lyrics: go to downtown if you're feeling sad)

Source: "Rebelové" (Rebels), a Czech 2001 retro-movie

Actress/singer: Ms Zuzana Norisová (*1979), Slovakia

English lyrics (a reverse translation of the retro-movie lyrics by a reactionary physicist L. Motl): "At Five O'Clock":

The hour is often rather patient / and then the Big Ben strikes five times.
I am thus singing here those silent words / that the fifth hour is gone: five times.

The bell is ringing, school is over / kids are running downstairs.
Mr Novák climbs apple trees / he's suddenly so fresh
what a mad day...

And I'm dying of laughter / someone is reproaching me and I'm not gonna cry
because

Five times. The Big Ben was just striking / Five times the Big Ben was just striking
Five times. The Big Ben was striking for us.

The last class often looks neverending / but then the Big Ben strikes five times.
That's why I'm singing you this unique song / that the fifth hour is gone five times.

The bell is ringing, school is over / kids are running downstairs.
Mr Novák climbs apple trees / he's suddenly so fresh
what a mad day...

[...]

The bell is ringing, school is over / kids are running downstairs.
Mr Novák climbs apple trees / he's suddenly so fresh
what a mad day...

And I'm dying of laughter / someone is reproaching me and I'm not gonna cry
because

Five times. The Big Ben was just striking / Five times the Big Ben was just striking
Five times. The Big Ben was striking for us.

[OK, I added the Big Ben because it fits perfectly. In the Czech version, "the fifth [hour] was just stricken". "Pátá" means "the fifth" (five o'clock, in this context) and it rhymes well with "five times" which allowed me to invent this brilliant text haha. Also, I am not quite certain that the poor kids had classes up to 5 pm or just five different classes. But a long day up to 5 pm seems more appropriate for this dramatic song. It reminds me of some of my crazy childhood days, too.]

---

Czech lyrics: "Pátá":

Hodina bývá dlouho trpělivá / a potom odbíjí pátá.
a tak tu zpívám slova mlčenlivá / o tom, že pomíjí pátá.

Zvonek zvoní, škola končí / po schodech se běží
Novák leze po jabloni / a je náhle svěží.
Bláznivej den...

A já smíchem umírám / kdosi mě kárá a páni
já nenabírám, neboť

Pátá právě teď odbila/ Pátá právě teď odbila
Pátá právě teď odbila nám

Hodina bývá někdy nekonečnou / a pak už odbijí pátá
a proto zpívám píseň jedinečnou / právě, že pomíjí pátá.

Zvonek zvoní, škola končí / po schodech se běží
Novák leze po jabloni / a je náhle svěží.
Bláznivej den...

Zvonek zvoní, škola končí / po schodech se běží
Novák leze po jabloni / a je náhle svěží.
Bláznivej den...

A já smíchem umírám / kdosi mě kárá a páni
já nenabírám, neboť

Pátá právě teď odbila / Pátá právě teď odbila
Pátá právě teď odbila nám / Pátá, pátá /fade out/

Georgia attacks South Ossetia

Previous article about a similar topic: Abkhazia

South Ossetia eventually became the first region, ahead of Abkhazia (that is of course also getting ready), where the conflict erupted a few hours ago.

The region won the independence from Georgia after the 1991-1992 War for Independence. In 2006, the de facto independent republic of South Ossetia held a referendum about the independence. 99 percent of the votes were in favor of the independence from Georgia.

Now, the Georgian government launched attacks against South Ossetia: see Google news. A few hours later, Georgia announced full military mobilization and declared a 3-hour ultimatum in which the civilians are demanded to leave their capital city.

You can see that pretty much all the events are isomorphic to the situation in Kosovo a decade ago except that the Albanians' claims for the territory of Kosovo are much weaker, both from the democratic as well as historical perspective, than the Ossetians' own claims for their independence.

Nevertheless, there exists a stunning degree of hypocrisy and double standards among most Western journalists and even the politicians. So don't expect that these folks will be celebrating the new Ossetian independence or organizing international tribunals for the Georgian aggressors.

When two peoples are doing the same thing, it's not the same thing, is it? Everyone has the same rights but some people are "special", aren't they?

As in most cases, the U.N. is useless. Even Russia's modest recommendation to both sides "to renounce the use of force" (a declaration that would be useless, anyway, but at least something for peace) has failed because the U.S., the U.K., and a few others joined Georgia in arguing that it is suddenly a great idea to use force. Wow. ;-)

Thank God, NATO has a more sensible (and peaceful) opinion and demands an immediate end to the Georgian aggression.

I kind of admire the Russian relatively calm approach and calls for peace on both sides - only a small region (with population of 70,000 only) is at stake, after all - but I would fully understand if they use jets to neutralize the aggressive portions of the Georgian "police" who are killing peacekeeping troops, among others. And maybe even the tanks.

I normally oppose most separatists but there is no God-given degree to which the separatists should be allowed to achieve their goals. The degree depends on immediate power and international conventions. Some recent events have (unfortunately) increased the rights of the separatists, as defined by the international conventions, and I consider self-consistency of the rules to be much more important than particular values of the "rights" that are assigned to the separatists. That's what precedents are good for.

Why is it sensible to assign importance to precedents? Because in legally complicated situations, it helps the expectations of various sides to converge. And if different sides share their expectations what would happen in a given conflict, they don't have much interest to start the conflict - at least not both of them. ;-) If they have similar expectations, it is much more likely that they will agree upon a peaceful solution.

Precedents help to define the rules of the game and maintain the stability and peace. On the other hand, any "adjustment" to the unwritten rules can lead various sides of conflicts that had stopped to recalculate and reopen their old conflicts. Of course, there can be a few other places where the Kosovo precedent will lead to new violence but I hope that some of the people will learn their lesson afterwords.



The president of Georgia ate his tie on live TV. It seems rather likely that when Saakashvili was a student at Columbia University, Peter Woit was his lecturer in discipline.

At this moment when it is clear that Georgia can't treat South Ossetia in a human way, it is becoming logical that Georgia will have to sacrifice this region. Let's hope that the casualties will be low.

LHC will be launched on September 10th

The New York Times inform about the date. By the way, all sectors are now at 1.9 K or so except for 81 that warmed up to 3 K in average again...

Original text (August 2nd, 2008):
27 pretty hi-res LHC pictures

Photos: see Boston Globe (click!)

See also LHC panoramic pictures, LHC alarmists about the irrational hysteria, and the LHC category of articles.

All sectors except for 78 are at 1.9 K. The sector 78 is still at 4 Kelvins, too hot.



Sorry, this blog will be silent (and pre-moderated) for a week, until next Friday: vacations in North Africa. Meanwhile, have a nice time, especially the friends in the TRF community!

SoCal: global warming escalates: 433 °C

FoxNews has a very interesting "most read" story at this moment.

LA Times add a map and a video

As you know, the climate warmed up by something like 0.6 °C during the last century. But as Marx Gore and Hansen Engels warned us, the warming would escalate.



Ladies and Gentlemen, the moment is here. Places in Southern California have warmed up to 433 °C (812 °F). I am curious about your explanation - probably related to geology and volcanoes that are nearby.

The authors of 10.5 apocalypse who envisioned the continental drift to be sped up by a factor of one trillion may have underestimated Mother Nature, too! ;-)

In the poll above, dozens of people have answered that the 812 °F heat is caused by the greenhouse effect. It would be interesting to know how many of them were kidding and how many of them are true hardcore nuts who are still able to open this blog. But we will probably never know. ;-)

Dixon law firm: CyberSUSY

John Dixon from the Dixon Law Firm in Calgary submitted the first, 40-page-long preprint about CyberSUSY. He plans to write and submit four papers and they should have hundreds of pages in total.

His law firm sounds even better than a patent office and because he claims to calculate the fermion masses and solve the cosmological constant problem, among other things, I couldn't resist to look at the paper. It would be pretty easy for me to overcome all kinds of idiosyncrasies if he had something to say.

Unfortunately, five minutes is enough to transform the eager expectations into a laughter. What does he claim to do?

He claims to have a framework that breaks SUSY at the same moment when the electroweak symmetry is broken. That surely sounds impossible but you don't want to give up too early. So you read how he intends to realize such a heroic tour-de-force.

Dixon modifies the supersymmetry transformations by adding new terms that have a simple impact on some particular composite operators in the theory. After going through 10 pages, you may finally see that this is his strategy.

Cracks appear soon

However, when you want to know what exactly happens, several explosive surprises are waiting for you. First of all, the modified transformations are BRST transformations. That's not what you would expect because the BRST transformation is a technical tool to deal with local symmetries, not with global symmetries such as supersymmetry in the supersymmetric standard model.

Such an observation will shock you a bit so in order to check whether you're on the same frequency, you return to his definition of the "normal" BRST transformation at the beginning of the paper. And your surprises continue. His "BRST" transformation is schematically equal to "C" times "Q". Now, I suppose that "Q" is the supercharge because of its spinor index and declared dimension. Clearly, "C" must be the parameter of the supersymmetry transformation for the variation to be a variation: it has the dimension "-1/2" and a spinor index, too.

Now, it's clear that Dixon has confused the supersymmetry parameters with the BRST ghosts "C". As a result, he has also confused supersymmetry transformations and BRST transformations. He still requires this (inherently) supersymmetric transformation to be nilpotent. ;-)

That's not an excessively promising mistake at the beginning of a paper that tries to derive a new kind of supersymmetry breaking from deformations of SUSY or BRST transformations. But such bizarre things continue. For example, even though Dixon claims to link SUSY breaking to gauge symmetry breaking, you will see no gauge fields or gauge transformations anywhere in the paper. ;-)

Also, the additional terms for the transformation rules are only written down for some composite fields, not for all (elementary) fields. The actions don't depend on the ghosts "C" at all which makes it less surprising that he manages to make his "BRST charge" nilpotent.

The cosmological constant problem is "solved" by looking at leptons only: gravity, gauge fields, and other fields seem to be "irrelevant" in Dixon's opinion. After 10 minutes, you see that the paper is complete balderdash and you stop reading. But there are several universal incredible patterns of papers written by these amateur scientists (a category that also includes lots of professional amateur physicists) that I want to describe explicitly.

Physics vs formalism

In real physics, one has to have an idea that can be described in physical words. The idea has to refer to actual physical objects - particles, black holes, fields, other measurable quantities, and physically verifiable symmetries and phase transitions, among other things. Once the idea or the problem is formulated, it must be refined and investigated by mathematical tools (such as the BRST formalism or others) that take over.

These mathematical tools are not "canonically" connected with the physical statements and questions but they nevertheless decide whether various hypotheses are correct and what the results are. The mathematical tools to find the answers are usually not unique (there typically exist many equivalent ways to obtain a result) but they are always essential. Sometimes you are led to an interesting equation that determines an observable quantity.

In amateur physics, at least the subtype of amateur physics that doesn't avoid equations, it is the other way around. They start with a program that is defined in terms of a mathematical object that would normally be just a tool to study physical assertions: a slave becomes the master. I am talking about the BRST transformation, a superconnection, etc. The physical propositions, physical starting points, and links of their new work to the existing laws of physics are completely missing. You can also see that simple mathematical objects such as algebraic equations or numerological identities are at the very center of their work while the other "calculations" are mostly added as a sort of decoration.

They do something with these mathematical objects that makes no sense and finally they "arrive" to grandiose statements such as "we have found a theory of everything" or "we have calculated the fermion masses" and "solved the cosmological constant" etc. You can see that most of these assertions were formulated long before they wrote the equations - the decoration. ;-) But it is not possible, not even in principle, to solve any of these problems by following a similar path.

To do anything sensible in theoretical physics, one must actually begin with a well-defined physical framework, modify some of its components or assume something about its parameters and initial conditions according to rules that can be motivated in physical terms, use mathematical tools to calculate the results as carefully as we can, and end up with some conclusions that couldn't be known at the beginning.

Consistency checks inside the text

Another thing that the amateur scientists seem to misunderstand is that it typically takes a few minutes to see that their paper is balderdash. They seem to believe that another physicist has to read every word of the paper, evaluate it for the same long period of time that they spent by writing the paper, and only afterwords, the physicist has a chance to have an opinion about the paper.

That's not how it works in reality. The meaningful papers in theoretical physics are actually not composed of 100% of completely new information. Quite on the contrary. Something like 1/2 of sentences in a typical paper are actually consistency checks in which the reader can verify that the author of the paper is not on a completely wrong track: the reader may check that what the author is saying is consistent with some of the previous, limited knowledge of the reader (either standard knowledge or other results in the same new paper), but the author can also add something new.

For example, when a new, more universal expression is given for a physical quantity (a function), the paper typically checks that the quantity is well-behaved in some special regime that should have been known before the paper was written. The author is supposed to be "a few steps ahead" of the reader and to help him to get through (imagine two mountaineers). When they don't share anything from the previous trip, that's already too bad.

Even more importantly, whenever there is something that seems to be a contradiction, a meaningful and well-written paper typically explains the subtlety that actually resolves (or might resolve) the contradiction. The author and the reader don't have an "identical" understanding what is surprising and what is expected about science but because they live in the same world with the same existing knowledge about the discipline, their expectations shouldn't be terribly different. If they're too different, it becomes impossible for the reader to read the paper.

But of course, the author is not obliged to pedagogically explain the fate of apparent contradictions etc. I wouldn't call the the resulting paper "well-written" if no attention is paid to important cases and possible contradictions but it could still be a "correct" paper, in some sense.

However, the amateur physicists are using the physical concepts in such a wrong way that it becomes immediately clear that they don't know what they're talking about. They don't actually omit the checksums. They include them and virtually all of them are wrong. For example, Dixon

• shows that he thinks that the BRST operator is a physical object in global SUSY model; in reality, it shouldn't be there at all, and even when one uses it, it is just a technical tool to deal with other symmetries and physical objects, not a "primary" object to build a paper upon
• confuses the BRST operator with the supersymmetry transformations
• in doing so, he checks the "nilpotency" of the supersymmetry transformations, instead of the correct (nonzero) anticommutators
• links supersymmetry breaking to gauge symmetry breaking but gauge fields don't seem to appear in the paper at all
• claims to solve the cosmological constant problem without talking about lots of objects (such as gravity and loops of particles) that are clearly necessary to say something about the value of the cosmological constant (electrons only are not enough)

and so on and on and on. So a meaningful scientific paper has 1 byte of new information followed by 1 byte of checksums. And the checksums must work correctly in 90+ percent of the cases, otherwise the paper is thrown away as gibberish. However, in Dixon's case, about 90 percent of these checksums are wrong.

Moreover, I believe that e.g. Dixon must completely realize that he has no clue what e.g. the BRST operator is. When most people are shown the BRST formalism for the first time, they don't understand why the details were chosen in this way. At the beginning, the BRST framework looks like a mysterious gift from the aliens. (See some motivation starting with the Abelian case.)

So I would personally never use the BRST formalism if I didn't know why the terms are what they are, why the operator should be nilpotent, and why the physical states should be the cohomologies. Dixon clearly doesn't understand most of these things. So why does he use this technical tool in his preprint? Does he really believe that it is possible to end up with anything meaningful if one uses tools that he completely misunderstands? It's like a native of a cargo cult tribe who pilots an airplane. The results simply can't be good.

Building a TOE from the scratch

In principle, you could imagine that an ingenious author writes an important paper that is completely disconnected from (almost) all the previous knowledge about science. You could imagine that the new genius would need no shoulders of the giants to stand upon. It has never happened in the history of physics but if such a thing occurred, the genius would still have to offer his own replacement for all the physical laws that have been verified and that he ignores or rejects.

Such a paper would have to be much longer - thousands of pages - and it would have to refer to a lot of experiments. Why? When you claim that a theory properly reproduces certain phenomena in physics, you must link the theory to experiments. It either means that you link it directly or, more typically, that you link it to some other papers and approximate theories and principles that have already been verified to agree with the relevant experiments: you normally link your new theories to the observations indirectly.

But if you want to avoid the existing state-of-the-art theories, the latter option evaporates. Your paper would have to talk about the experiments themselves and it would look very different from Dixon's paper.