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?

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.

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”.

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)

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.

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.

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