## Sunday, July 01, 2012 ... /////

### An interview with Arkani-Hamed on SUSY

Higgs news: The Daily Mail claims that CERN will only announce 4-sigma near-discoveries on Wednesday, short of the 5-sigma discovery claim. Of course, two single-detector 4-sigma claim imply a 6-sigma overall evidence for the God particle. Five God particle founding fathers were invited to the seminar so you may better buy the "I $\heartsuit$ Higgs" T-shirt now.
A reader nicknamed Synchronize has brought my attention to this almost excellent Science Watch interview with Nima Arkani-Hamed.
Nima Arkani-Hamed on maximally supersymmetric theories
They start by explaining that Nima is a big shot who doesn't belong to the bottom 99%. He says that SUSY is so fundamental that everyone works on that in one way or another. Then he criticizes string theorists for having been insufficiently stringy some years ago – for spending too little time with the most marvelous and supersymmetric vacua such as one described by the maximally supersymmetric gauge theory relatively to the more complex and less supersymmetric compactifications.

In a rather technocratic method – which is surely superior in comparison with the bullshit promotion of crackpot papers by the armchair physicists in the media – they ask Nima about his two most cited papers in the last decade (so that the large extra dimensions are excluded).

They're papers about deconstruction which just doesn't happen to be too closely related to SUSY although his paper with your humble correspondent and three others applies deconstruction to some stringy theories, including the (2,0) theory and little string theory, where SUSY plays a crucial role.

The interviewer couldn't quite see that the first top-cited papers are closely linked to one another, either, so the predecided structure of the interview didn't end up being quite as smooth as the interviewer may have expected.

Nima mentions some cool properties of the maximally supersymmetric theories, the harmonic oscillators of the 21st century, and says that he is not much more worried about SUSY at the LHC now than he was before the LHC was getting started – because some signs that SUSY wouldn't be behind the corner were already available (I am a witness to this claim, having listened to Nima's opinions about these matters for years). In a few years, we will have the final answer on whether or not the lightness of the Higgs boson is explained by a natural mechanism such as natural SUSY in the sense many of us believed. There won't be any more babbling about this issue, just some new cold hard facts...

At the end, Nima refers to some cool links between these physical theories and some very advanced mathematics that he's been obsessed with in recent years.

#### snail feedback (25) :

"There’s a remarkable connection between some very deep ideas in
mathematics that are starting to emerge. These are really startling
connections between the dynamics of gauge theories and conjectures in
mathematics that are related to the Reimann hypothesis." I guess he refers to the RIEMANN hypothesis here.
But in what way RH affects dynamics of gauge theories,what he is talking about?

I found a cool review paper about the Riemannian hypothesis in physics
http://arxiv.org/pdf/1101.3116v1.pdf

Hi Lubos,

Good to see some of this information on Supersymmetry as I had thought somehow it had all gone away.

The maximally supersymmetric theory in 4 dimensions is N=8. But don't we already know, or suspect, that it diverges beyond 7 loops, has bad UV behavior, must be UV completed, cannot describe the entropy of a black hole, etc? So why is he so interested in this stuff?

Yes, cool. Thanks for that Mephisto. I love papers that have history embedded in them and the paper is clear and not written in Gaussian tricks of leaving out all steps that are "trivial":) (Hardy apparently was giving a lecture and writing equations on the board and at a step said "it is trivial to get this result", stopped, looked thoughtful, then abruptly left the lecture theatre. He returned 20 minutes later with no explanation and said to the students "Yes, it's trivial".

Dear Ghandi, he mostly means - and he's mostly studied in recent years - the maximally supersymmetric gauge theory which has N=4, no gravity, and no problems with nonrenormalizability. It is actually an exact description of string theory on AdS5 x S5, among other roles.

This paper shows how often special functions appear in treatments of various problems in physics and Zeta function is met there quite often too.Well, I knew that already.Interestingly, the paper doesn't stress Zeta function has many other interesting properties -important both for math and physics,other than distribution of its zeroes . So why is RH important for gauge theories isn't clear to me.

"Quantum physics sheds light on Riemann hypothesis."
http://www.maths.bris.ac.uk/research/highlights/random-m/

"In their search for patterns, mathematicians have uncovered unlikely connections between prime numbers and quantum physics. Will the subatomic world help reveal the elusive nature of the primes?"http://seedmagazine.com/content/article

Not to mention The Hitchhiker's Guide To The Galaxy.

Dear Plato, why did you exactly think that SUSY "had but all gone away"? This is completely insane.

If you look at the hep-ph (phenomenology) papers right now,

http://arxiv.org/list/hep-ph/new

you will see that SUSY is the very central focus of at least 7 papers (out of 26), including the first and third one - and people typically try to post important papers so that they appear near the top so the ordering isn't quite irrelevant.

A rather typical daily dose. SUSY is clearly the single most important principle of new physics that people study. It's perhaps even more important in hep-th

http://arxiv.org/list/hep-th/new

Thanks for your comments. The paper you mentioned says they will study the "UV properties of N=8", but I can't see what, if anything, they actually say about its UV properties. Isn't it clearly sick in the UV?

Also, can you elaborate on what you mean by its "classical structure"? What are its classical properties? Are you thinking of just treating it as a classical field theory? If so, what do I do with the "classical fermion fields"? On the other hand, perhaps you just mean the tree-diagrams? But these refer to scattering of point particles, right? But aren't the point-particles "quantum states" from the perspective of the field theory? Or perhaps you mean a mix; where I treat fermions as point particles, and bosons as fields? Is this the "classical" description? Sorry, for my silly questions; this point confuses me. Thanks for your help.

Is it possible that SUSY is just a grand unified theory of abstract spaces?

Not sure whether this is a serious question or just some joke I didn't get but if it is the former, the answer is No.

SUSY is in no way just a "theory of spaces". SUSY is primarily a framework for physical theories. It's the phenomena themselves that are supersymmetric or non-supersymmetric, not just some abstract spaces.

SUSY unifies bosons and fermions, in some sense, but otherwise it's completely wrong to call it a unifying theory, too, especially not a unifying theory of possibilities or spaces. SUSY doesn't "unify" anything aside from bosons with fermions - and surely not "everything". SUSY is an extra constraint that implies that almost no one has the right to join the elite club, almost no one has the right to be "unified" with it. So even at your vague level, I think that you got everything upside down.

Dear Ghandi, the paper is available here:

http://arxiv.org/abs/arXiv:1202.0014

I think that these folks mean by "UV properties" primarily the question whether the SUGRA theory is perturbatively finite and they're among the world's leading believers that it is.

"Classical structure" are indeed properties visible in the classical limit. In the classical limit, fermions are treated classically - you may still calculate Poisson brackets, Hamiltonians etc. - but if you ask what a value of a fermionic variable is, it is classically zero. A fermion is really proportional to sqrt(hbar) so it must vanish in the classical limit. After all, no c-numbers anticommute with each other but the "classical values" of fermionic fields would have to anticommute.

There is no problem with point-like particles. When we study the classical structure, yes, we mean tree-level diagrams which contain information equivalent to the classical field theory. This has no states with quantized energy E=hf - particle-like - because h=0 but it's still called a point-like particle field theory because normal field theories lead to point-like particles upon quantization (and we know that even if we don't quantize them).

Elite in a huge landscape is not L33t at all, no? I am more interested in looking at the broader implications of the kinds of spaces that are allowed by SUSY and those that are duals to logics via generalizations of the Stone duality.

An elite is always an elite. The previous sentence is a tautology and your disagreement with it means that you have problems with basic mathematical logic. The elite character has nothing to do with the size of any landscape. Moreover, the supersymmetric theories primarily discussed here are completely unique for a choice of discrete data (e.g. the gauge group of an N=4 Yang-Mills theory).

Also, it is nonsensical to talk about "broader implications" if you're only interested in "spaces allowed by SUSY". Spaces allowed by SUSY - if this concept is well-defined at all - is an extremely narrow aspect of SUSY. SUSY is much broader a system of idea than your extremely limited caricature of it.

The relevance of "Stone duality" for SUSY seems to be pretty much zero, too.

"Then he criticizes string theorists for having been insufficiently stringy some years ago ..."

Ts ts ts ts ts ... this makes me shaking my head chuckling in amusement ;-) :-P :-D

Nice interview and I like Nima' s very interesting answers a lot :-)

At 14h00 there is the tevatron webcast. How good chances are of having some surprise?

Thanks, Cesar. The webcast starts in 10 minutes from now here:

http://vms-db-srv.fnal.gov/fmi/xsl/VMS_Site_2/000Return/video/r_livelogicindex.xsl?&-recid=634&-find=

Thanks for your helpful response. But let me clarify, so are you saying to just set the fermions to zero? This would be confusing, because the tree diagrams exist even for fermions. By the way, what about the grassman variables, can they be used in the "classical" theory? Also, how to describe quantum states, like the superposition of 2 classical states; can this be connected to tree-diagrams?

Dear Ghandi, the tree level diagrams with fermions have the same shape as for bosons and they may be calculated by the same approximate leading, "classical" approximation (Poisson brackets instead of anticommutators etc.) but the correlation functions they express are formally proportional to a higher power of hbar.

So the very appearance of a fermionic line in a tree-level diagram means that it encodes some quantum phenomena. This argument is equivalent to noticing that one can't have a macroscopic "vev" of a fermionic degree of freedom - simply because a macroscopic classical wave is a condensate of many particles in the same state but for fermions, this is prohibited by the Pauli exclusion principle. So a third, equivalent way to phrase these things is that the fermionic degrees of freedom are "obliged" to remain infinitesimal. theta^2=0 valid due to the fermionic statistics may also be compared with the negligible size of second-order quantities which are higher powers of infinitesimal ones.

So once again, one may talk about Grassmann numbers but they're a formal algebra and the numbers can't have any "classical values" different from zero even if we can do analogous algebraic steps with them. This is linked to the fact that the occupation numbers for bosons are positive integers - in the classical limit, they may be approximated by a real number. For fermions, only N=0 and N=1 is possible and these two values are "infinitely close" to each other in the continuum limit so they can't be distinguished in the classical theory. So the fermionic_fields=0 is the only single state of the fermionic fields in the classical limit. The very appearance of particles from fermionic fields is a quantum effect so it's no longer a part of the tree-level analysis of a QFT.

Thanks again for your answers. In your final comment, you say "The very appearance of particles from fermionic fields is a quantum effect so it's no longer a part of the tree-level analysis of a QFT". I have 3 follow-up clarifications on this point: Firstly, is this statement true for both fermions and bosons? Secondly, we often use tree-diagrams to compute things such as electron-electron scattering, and it is often stated that this gives the "classical" answer; so how does this fit in with your comment that "it's no longer a part of the tree-level analysis of a QFT"? Thirdly, if I examined scalar-scalar point-particle scattering, would this be part of the tree-level analysis? Thanks.

I'll have to search for the video, but I know Nima Arkani-Hamed once said at a public lecture that sometimes he thinks that we' won't find the surprising stuff like extra dimensions, but we will find supersymmetry, while other times he thinks we'll find extra dimensions as well. It's really funny to see how now that the LHC has completely obliterated any hope of a SUSY discovery that he says it's no big deal. When will people listen to Woit and start studying other ideas? I think he's right that as soon as somebody comes up with a real idea they'll drop SUSY pretty fast.

No, the statement containing "fermionic fields" is only about fermionic fields. Obviously, the appearance of a large number of particles in bosonic quantum fields - a condensate that becomes macroscopic - is the way how classical bosonic field theory emerges from quantum bosonic field theory. Please read e.g.

http://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html

Yes, the electron-electron tree-level scattering is classical answer in the sense that it's the leading term in hbar, without any hbar corrections; it's just a terminology - we call the tree-level corrections classical because they folllow a similar simple algebra "without integrals" that would calculate a classical expression. But that's it. It's not classical in any other sense.

The fact that we call something "classical term" for a good reason doesn't mean that the underlying theory has all the properties of a classical theory in physics. It doesn't. In particular, a classical theory doesn't have any discrete states (with electron vs. with no electron). Classical limits of all such theories have continuous variables. The occupation numbers for bosons may be large and become effectively continuous; however, for fermions, they're just 0 or 1 which cannot become large and in the classical "continuum" limit, they are indistinguishable.

Concerning the third question, tree-level diagrams are tree-level diagrams. By definition, we call them "classical terms", scattering with the adverb "classically", and so on. The only negative statement I've been telling you is that the existence of these discrete particles themselves can't be extracted from any classical theory - it's a quantum phenomenon - and in the case of fermions, classical field theories can't even have any nonzero expectation c-number complex or real value of the fields, either. I don't quite understand what is so unclear about these things.