Tuesday, December 07, 2004

Unity of strings

Peter Woit is planning to create a permanent clipboard - or a macro - with a disclaimer that divides string theory into two pieces: a "useful toolkit" and a "colossal disaster". Because this macro is gonna be permanent, it may be useful to explain why it's inconsistent. This article will first quote Peter Woit who described his viewpoint on these issues in the "Comments" section under one of his articles, and then it will explain reality.

Peter Woit wrote:

I suppose I should write a macro so that whenever I write anything about the disastrous effect of string theory on particle physics it includes the disclaimer:

1. No, I'm not talking about the effect of string theory on mathematics, which, on the whole has been very positive.

2. No, I'm not talking about the idea of using string theory to get information about strongly coupled gauge theories, which has had some real successes.

3. Yes, I am talking about the idea that there is some fundamental 10 or 11 dimensional supersymmetric theory of extended objects which explains both quantum gravity and the standard model.

It's clearly point 3 that Krauss was referring to as a "colossal failure" and anyone who has read more than a few postings on this weblog would be well aware of points 1,2,and 3. The NYT article was not about whether string theory was successful as mathematics or whether it was promising as a way to solve QCD. It was very explicitly about the status of string theory as a unified theory and that is the issue to which my posting was addressed.

The view, prevalent among more than a few mathematicians, that since important new ideas about algebraic geometry and other parts of mathematics have come from work motivated by string theory, there must be something to the idea of string theory based unification of gravity and particle physics, seems to me to be deeply superficial and essentially uninteresting.

... I don't think I've made an error in logic. Thinking about 10 or 11 d strings/M-theory may lead one to interesting things (in math or gauge theory) even though your original motivation turns out to be a wrong idea.

Actually, I think string theory has been such a success as math precisely because it has failed so badly in its original motivation. If in late 84-early 85 people had found some Calabi-Yau and some version of string theory on it that allowed the calculation of the parameters of the standard model, mathematically the whole field of string theory might have lead to a lot of information about one Calabi-Yau, and not much else.

Because string theory doesn't work as intended, string theorists have spent 20 years thinking about a wide array of mathematically very complex and rich structures. Coming at these structures from a very different perspective than the traditional mathematical one has lead to a lot of interesting new mathematics. The colossal failure of the string theory unification project as physics has ended up benefiting mathematics quite a bit.

Urs Schreiber's comment:

Peter's comment reminds me of that scene in Monty Python's "Life of Brian" where they ask

  • "What did the Romans ever do for us?"
  • Yeah, what? Apart from...

My answer to Peter Woit

It is impossible to divide string theory to the groups 1,2,3 explained in Peter Woit's text: string theory is a unified, rigid structure that cannot be separated to pieces and cannot be separated from many physical and mathematical questions affected by string theory's insights. The successes included in the groups 1,2 did follow from very specific questions that were asked as string theorists tried to use their unified theory to answer various questions about quantum gravity and the Standard Model.

It may be useful to mention particular examples showing why nearly all of these positive effects of string theory on our understanding of strongly coupled gauge theories and on mathematics were derived from string theory visualized as a unified theory of quantum gravity that includes gauge theories with fermions etc. such as the Standard Model but also 10- and 11-dimensional vacua with extended objects:

Gravitational duals of gauge theories

The strongly coupled limit of the gauge theory, according to the AdS/CFT correspondence, is a theory of quantum gravity. For example, the N=4 d=4 super Yang-Mills is equivalent to type IIB on AdS_5 x S^5 (note that 5+5=10 which is the critical dimension of superstring theory). In early 1998, Peter could have said that it is just type IIB supergravity, except that today we know a plenty of ways how we can see that the gauge theory is dual to the whole of string theory, including the excited strings. The closed strings are dual to operators like Tr(ABCDNBBBBCSB) where the letters are fields in the adjoint representation and one can reproduce their correct spectrum (this is especially well understood near the Penrose limit of the anti de Sitter space times the sphere), interactions, as well as the spectrum of branes of various dimensions from the gauge theory.

The same statement holds for the strongly coupled dual of any other theories that are studied, and if you ask sufficiently deep questions, you're guaranteed to need the whole string theory. The quantum gravitational phenomena that you can see from the conformal field theory include topology change inside asymptotic AdS spaces, see Maldacena et al. recent paper, as well as black hole thermodynamics and other things typical for "quantum gravity". Maldacena originally discovered his holographic duality because he was thinking about the regularities in string theory's explanation of the black hole entropy - which is, no doubt, a typical example of an insight that connects string theory as a theory of quantum gravity to various universally believed facts about the observable Universe. Black holes are seen in the telescopes, after all, and the arguments that they carry the precise entropy are rather strong.

In fact, the motivation from string theory in the late 1960s was to describe the strong interaction - a very material, testable portion of particle physics. When QCD was found, this original motivation of string theory was declared false - but in a sense, the whole AdS/CFT business is about reviving the old idea. Dynamics of QCD - and especially other theories - is equivalent to string theory in some background. This background is known for some gauge theories and many people are trying to extend their understanding to other gauge theories and phenomena, too.

Mirror symmetry

Mirror symmetry, an example of string theory's influence on mathematics, is a relation between two Calabi-Yaus that look geometrically different, but give you the same physics if you compactify string theory on them. By "physics" I mean that they will predict identical results for scattering of gravitons and Standard-Model-like quanta if you use the Calabi-Yaus as compactified manifolds. The Calabi-Yau compactifications are exactly the same compactifications that were used for 10+ years as the unique way to derive the real Universe - the Standard Model (or SUSY GUT) plus quantum gravity - from string theory. The realistic vacua are really obtained from the heterotic strings while we often study type II strings on Calabi-Yau in the context of mirror symmetry, but most of the results are analogous. The mirror symmetry was found because the detailed properties of the Calabi-Yau spaces and their orbifolds were studied - and they were studied exactly because these Calabi-Yau compactifications and their orbifolds lead to realistic physics in four dimensions.

If you want to study some mathematical questions about the geometry of Calabi-Yaus only, you may truncate the full string theory onto topological string theory. It still has a lot of stuff, but it's clearly just a truncation, and all string theorists that work on topological string theory realize that there is a lot of stuff in string theory outside topological strings. I believe that many mathematicians realize it as well, although the truncation is sufficiently interesting for them to treat it as the "better established" part of string theory.

All these dual stringy pictures to tasks in mathematics and gauge theories are very specific configurations in the full string/M-theory, and it is absolutely impossible to understand their physics and mathematics correctly without knowing that there is a consistent theory of quantum gravity that admits 10- or 11-dimensional vacua but that also predicts gauge-theory-like matter in its various compactifications. Many of these dual insights can be used to show not only that the critical dimension of string theory must be 10 and 11 for M-theory, but many much more detailed facts about string theory - and all these pictures fit together.

It is impossible - or "false" - to split string theory into pieces that don't talk to each other and that don't share ideas. The ideas of string theory are unified and one can't separate them into subfields that can be meaningfully studied in isolation.

Nothing guarantees that string theory will be proved to be an exact theory describing everything in this particular Universe. On the other hand, the assumption that something like that is possible has been a necessary driving force that has also led to the insights that Peter Woit accepts as success stories. They were not just a driving force: the particular physical intuition - often the same intuition that is needed to derive the actual observable physics from string theory - was necessary to find those great results.

Successful physics vs. successful maths

Peter says that the successful mathematics could only arise from string theory because string theory failed to calculate the properties (like the masses) of the elementary particles in the middle 1980s. It's difficult to imagine where the world would be going if the "theory of everything" were completed in 1985. It may still be the case that there exists an old-fashioned Calabi-Yau and a relatively simple calculation, more or less doable back in 1985, that reproduces the real world. Imagine that it is the case. If people had found it in 1985, the following things would have probably happened:

  • The critics of string theory would have disappeared from the academic discourse and they would be generally viewed on more or less equal footing with the anti-relativity crackpots, for example.
  • Even though the final theory of this Universe would have been found, it would not stop the research in high-energy physics. Every good answer opens five new questions in physics. Thousands of new people would start to study various consequences of the new precise stringy picture of the Universe. The funding would increase drastically, and a triple SSC would be built quickly.
  • Because the number of people would be so much larger with this discovery, I guess that some of them would study the questions of different compactifications, T-duality, D-branes and so on anyway. Note that even with a specific Calabi-Yau manifold found to describe the real world, it should still have a mirror dual! I don't really see any reason why people should not have discovered mirror symmetry. Also, I see no reason why they should not have tried to answer the questions about black hole thermodynamics because it is a part of physics regardless of the success of failure of our calculations of particles' masses.
  • Although the fraction of the people who would study the mathematical aspects of string theory as opposed to direct links with observable physics would be much smaller than it has been in reality, the absolute number of the people who would study mathematical aspects of string theory - and other compactifications (i.e. other real Universes disconnected from ours) - would not be smaller, and they would have made the same discoveries we have made.
I just think that knowing something usually does not hurt you.

1 comment:

  1. You cleverly ended with: "I just think that knowing something *usually* [my highlight] does not hurt you."

    Why it was clever, is that getting to know, or even just getting too close to becoming neurally connected in respect of certain facts/patterns of Reality (or tolerably certain aspects of What Is going on), CAN psychologically hurt/damage/disintegrate self.

    [And of course, as a psychosocial and/or physical extension of such a painful process NOT reaching a full and purely self-destructive completion, it can tear-down others as well. Suicide-bombers being just one gorily glaring example of this.]

    I'll keep entertaining myself with watching your search for the final self-evident definition of our not quite particular stringy vacuum, and your ongoing battle with the seemingly ever present "P[er(versely/turbative)] Woi(d)t".