Alexander Polyakov is one of the most prominent figures in theoretical physics and one of the most well-known string theorists at Princeton. He has written a review of his career and of his efforts to understand the relation between gauge theory and string theory. His penultimate paragraph goes as follows:

“In my opinion, string theory in general may be too ambitious. We know too little about string dynamics to attack the fundamental questions of the ‘right’ vacua, hierarchies, to choose between anthropic and misanthropic principles, etc. The lack of control from the experiment makes going astray almost inevitable. I hope that gauge/string duality somewhat improves the situation. There we do have some control, both from experiment and from numerical simulations. Perhaps it will help to restore the mental health of string theory.”

Seems to me he’s saying that, while using string theory to understand gauge theory is sensible, those claiming that it provides a theory of everything have gone nuts. I wonder what his colleagues at Princeton think of this.

Excuse me for pointing out the obvious, but if Motl, Hawking, or any other “genius” out there can’t back up speculations or half-baked science regarding black holes with a consistent quantum theory of gravity then I will continue to exercise my right to ignore them.

I’m sad to have to report that my contribution to Lubos’ education will not be shared with the readers of sci.physics.strings. Lubos replied that my contribution did not meet the high standards of his group [I wish you people wouldn’t snicker like that–] and that anyway it should be obvious why nobody cares about the observations of black hole observers who are not infinitely far away from one. In the immortal words of Peter Woit: got that?

Next question: whence this strange enthusiasm for Hawking’s work on the part of LM?

Ah, the famous Schroedinger’s soul problem!

By the way, in case anyone doubts the literal truth of Peter’s title for this section, you might like to have a look at Lubos Motl’s latest writings on sci.physics.strings. His conclusion is that we shouldn’t really worry about information loss since we are all gonna [sic] die anyway and *some* information will be lost in that way. Here is my response — it will be interesting to see how he behaves in his capacity as moderator:

Lubos Motl wrote in

>

> Yes, no one has really resolved and defined the correct laws of physics as

> seen by the infalling observers. Well, they’re gonna die which

> automatically means “some” loss of information from their point of view.

[My reply]:

Profound, truly profound. We’re all gonna die and that will mean

the loss of “some” information.

Thank you. My doubts about unitarity in quantum gravity have

all been answered.

On second thoughts, what if we go to heaven? Or, in

the case of some of us, to the Other Place? Will

unitarity be preserved by supernatural tunneling?

JC –

I haven’t looked at which calculations precisely Dixon does. But I am sure he said that he can relate QCD calculations of N=4 SYM and that hence any better understanding of the latter has an effect on the QCD calculations.

Urs,

Most of the stuff Dixon alludes to doesn’t appear to use the AdS-CFT duality directly. The most that appears in his strings 2004 talk that alludes to AdS-CFT, doesn’t look like it’s much more than hand waving. I didn’t see any explict AdS-CFT calculation results in his talk, nor in any of his previous papers. Where did you see Dixon’s stuff on explict AdS-CFT type of calculations?

In Dixon’s earlier work on calculating QCD amplitudes, SUSY appears to be used as a calculational “tool” and not really as a fundamental symmetry. How he’s able to this, I’m not entirely sure offhand. The only semi-plausible reason I can think of offhand is in the first quantization picture of gauge theories. There were a number of papers by Michael Schmidt (at Heidelberg, I think) from the 1990’s which looked at QED in the first quantization picture. Turns out the Lagrangian for first quantized ordinary QED has an explicit “SUSY” symmetry, which doesn’t readily appear in the textbook version of 2nd quantizated QED. In some sense, the first quantized picture of ordinary QED gives you a “SUSY” symmetry literally for “free”. Where exactly this SUSY symmetry comes from in the first quantized ordinary QED, I don’t know offhand. There’s a section in Polyakov’s book which discusses the first quantization picture for ordinary QED.

It appears Schmidt, nor anybody else yet, has been able to generalize this result to the non-Abelian gauge group case. In principle, a first quantization picture of ordinary Yang-Mills theory coupled to fermions, should reproduce the results Dixon got in his earlier QCD calculation papers that used SUSY as a “tool”.

Thomas –

there is string/gauge duality and it is best understood for cases which do not very much resemble the real world. N=4 SYM is best understood because of its high symmetry. That makes it easy. As Witten nicely explains in his intro to the Clay institute challenge on YM, the reasoning is as follows:

– we want to understand YM

– but YM is hard

– so as a first step move to a point in field theory space which is easier to handle

– this leads to the study of supersymmetric QFT and N=4 SYM in particular

– so let’s study this as a first approximation to what we are really interested in

– surprisingly it turns out that N=4 SYM is apparently equivalent to superstrings on AdS5 times S5 (this is a conjecture, true, which has been check to 2.5th order or something, pretty impressive already)

JC –

at Strings04 in Paris Dixon gave a talk on how to compute QCD stuff by mapping it to N=4 SYM. For instance, if I recall correctly, he said that the tree level amplitudes are the same when you identify the SYM fermions appropriately, and that similarly higher loops can be mapped in a certain way to SYM.

But once you are doing anything with N=4 SYM you can equivalently compute on the dual string theory side. For instance the recent progress in computing anaomalous dimensions in N=4 SYM is all based on BMN, spin chains, semiclassical strings in AdS5 and so on.

Urs,

I admit that I find the equivalence between N=4 SYM and gravity very confusing. However, this kind of correspondence only seems to work (if it does, Maldacena is still a conjecture, right?) for YM theories plagued by almost-falsified supersymmetry. I am positively sure that vanilla Yang-Mills, of the kind present in the standard model, does not contain gravity. The standard model is not a theory of gravity, is it?

I will come back to loop space gauge theories later.

Urs,

Lance Dixon’s work doesn’t appear to be using the AdS-CFT duality stuff. Most of Dixon’s results look like they’re perturbative amplitude calculations in Yang-Mills theory, using string inspired methods such as in his lecture notes hep-ph/9601359

Looks like Dixon’s later work on calculating gravity amplitudes via Yang-Mills results, appears to be generalizing a result between open and closed strings in Kawai, Lewellen and Tye’s paper “a relation between tree amplitudes of closed and open strings” Nucl. Phys. B, 269 (1986), where Dixon et. al. takes the point particle limit. The net result he found appears to be writing perturbative gravity amplitudes as the “square” of some corresponding Yang-Mills amplitudes. On the surface it appears that it’s an easy way to get gravity amplitudes by just recycling old Yang-Mills amplitudes calculated previously. There’s a review paper by one of Dixon’s collaborators, Zvi Bern, that reviews all of these perturbative gravity calculations without having to calculate Feynman diagrams directly by brute force from first principles gr-qc/0206071

Hi Thomas –

I should definitely learn more about gauge theory in loop space formulation and maybe you can teach me something. (BTW, did you see my reply to your SCT comment.)

Concerning YM in 4D and gravity I don’t understand what you are saying. The big exciting fact is that N=4 SYM is equivalent to a theory of gravity. People like Dixon are even using this to investigate QCD amplitudes by using recent results on strings in AdS. If you like this or not or if you think the dual gravity can have any relation to the gravity that we observe, it is still there.

Polyakov is probably my greatest living hero (Einstein and Dirac are unfortunately dead), so it makes me happy that he is ready to acknowledge problems in the string theory, despite his important contributions to that subject.

I don’t think that anybody has seriously questioned that gauge theories can be formulated in terms of stringy variables. This idea may go back to Faraday and his flux tubes, and it was completely clear with the introduction of Wilson lines in 1974. It is less clear to me how useful such a formulation is; the Migdal-Makeenko loop equations are now 30 years old and still defies any hope of solution. Loop space is really messy because it is so big.

However, Yang-Mills theory cannot be equivalent to string theory even if formulated in stringy terms, since it does not contain gravity and is consistent in 4D. There are of course close analogies between Yang-Mills and gravity, exploited e.g. in LQG, which is a loop space formulation of gravity in Ashtekar variables. But if you find gravity in Yang-Mills you must have done something more than a reformulation.

This always leaves me puzzled: I may acknowledge that strings know about gauge theory but I may not be excited about them also knowing about gravity? ðŸ˜‰

The QCD strings, old or new ones, are the most promising silver bridge for trapped physicists -specially for younger ones- to escape from string theory. It is not rare, from time to time, to heard invitations to use it. In this way it does not seem that you have been years in the blue; instead you can claim a consistent career path and keep going.