Terry Tao’s article What is Good Mathematics?, written for the Bulletin of the AMS, is now available at the arXiv.

There’s a new article also on the arXiv by Zvi Bern et al. explicitly constructing the 3-loop 4-point amplitude of N=8 supergravity. They find various extra cancellations beyond those expected from supersymmetry, and argue that this and other calculations “strongly suggest that N=8 supergravity may be finite.” The innumerable claims made over the years at the beginning of pretty much every string theory book or popular article that you definitely can’t quantize gravity just using QFT are now no longer operational. There is quite a lot of interest in this topic, with an array of possible computations that need to be done in order to sort this out. Just at the Mathematics Institute at Oxford the past few weeks there have been talks related to this by David Dunbar, Kellogg Stelle, Bo Feng, and Michael Green. The Resonaances blog has a report about a talk by Lance Dixon, one of the co-authors of the new paper. Also a nice report on a talk about supersymmetry by David Kaplan, who gives an excellent definition of fine-tuning of parameters: “a model is fine-tuned if a plot of the allowed parameter space makes you wanna puke” (accompanied by an illustrative plot of the situation in mSUGRA).

I’m waiting for the above news about supergravity finiteness to hit the media, perhaps some of the people working on this need to get to work on their press releases. There’s yet more press about the Distler et. al. “test of string theory.” The Daily Texan has an article called Test May Prove Far-out Theory, where Distler explains how the LHC seeing effects consistent with unitarity, analyticity and Lorentz invariance will provide “more evidence” for string theory. The reporter who wrote this called me up, and includes a garbled version of what I had to say. I was trying to be polite and stick to just pointing out that the paper at issue was not a string theory calculation and its title had been changed to remove reference to string theory, something I suggested the reporter might want to ask the paper’s authors about. He seems to have not taken up my suggestion. I probably should have just used more straight-forward language, something along the lines of “dishonest bulls**t”.

The US Congress finally finished dealing with the FY2007 budget, sending a bill to the president which he’ll sign. It restores money to the NSF and DOE, avoiding a freeze at FY2006 levels that looked possible for a while and would have forced shutdowns at Fermilab and RHIC.

Finally, Capitalist Imperialist Pig informs us that Princeton is taking the occasion of shutting down its parapsychology lab to also close down its string theory program and redirect the funds to research on global warming. Somehow I suspect this may be a bit of an exaggeration, but they do seem to be making moves away from string theory and towards phenomenology, sponsoring workshops next month on Physics at LHC: From Experiment to Theory, and Monte Carlo Tools for Beyond the Standard Model Physics.

**Update**: Here’s a link to the Kaplan talks on SUSY.

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Alex,

This isn’t an experimental question, it’s a purely theoretical one about whether these higher order terms are finite or not. In principle it’s a straightforward calculation, and one can just calculate. The problem is that the calculation is so difficult that people have to use indirect arguments and make some assumptions in order to get an answer at high orders.

Alex, from your comment it seems you think that the papers you link to are about two different theories, one stringy and one involving point particles. This is not the case. Both are about N=8 supergravity in four dimensions, they are just approaching it from different directions: you can get to this theory by compactifying 11D maximal supergravity.

In general the question of whether this is a “field theory of gravity” or a “string theory of gravity” is not well-defined. As with any interesting field theory, there are nonperturbative effects. In gravitational theories these contribute exp(-1/g) terms, which are understood in string theory to be associated with branes. So solitonic objects are inescapable in this theory, even if it is perturbatively finite. (The solitons are associated with the divergence of the

sumof the perturbative theory, which will diverge even if the individual terms are finite.) N=8 supergravity is part of the same family of theories as M-theory (the UV completion of 11D sugra), which includes both theories with light strings and those without.In any case, it certainly isn’t a typical local QFT of spin-2 objects, the usual difficulties with constructing local observables in quantum gravity apply to N=8 supergravity even if it is finite.

“The conventional wisdom that QFT’s involving gravity inherently have bad behavior in the ultraviolet looks like it is just wrong. ”

I don’t think this is the conclusion that the authors are claiming—in the last paragraph they seem to imply that stringy effects are still needed to get all of the cancellations needed:

“The result presented here, in conjunction with the allloop-order evidence from unitarity [13] and string theory hints of additional cancellations [7, 8, 9], strongly suggests that N = 8 supergravity may be ultraviolet finite.”

JustAnotherInfidel,

The reference is to independent duality arguments of Green et al. that do have to do with string theory, but have implications for pure supergravity. What is being discussed here is not string theory, it is a QFT, N=8 supergravity, and the question is whether the terms in this perturbation series are finite. String theory methods may be useful for showing this (although the Bern et al. paper under discussion does not use string theory), but the claims are being made about a theory that does not involve strings, and is a conventional QFT. It is precisely this conventional QFT that people have in the past believed had bad high energy behavior, but now it appears this may not be true.

I havent checked the blog for a while, but I would like to point out that it is straightforward to obtain a nonperturbative formulation of N=8. Take the nonperturbative formulation of IIB string theory compactified on a six torus and decouple the massive modes. I believe the exact S-matrix of IIB string theory is known, and for that matter, after decoupling the massive modes so is the exact matrix of N=8 sugra. Of course the exactitude of the S-matrix relies on the belief of S-duality

so consider it a hypothetical exactness until duality is shown.

By the way in case you are interested there do seem to be some early articles on obtaining the standard model with some technicolor type of arguments but that is all. The theory seems to be nonviable unless the standard model gauge group changes, which is in fact possible if you read some more about string bits.

Also, just as a plug, I am in fact the first person to argue for finiteness in a concrete manner, and to this day my arguments are

repeated almost by everyone except for Bern et al, who use the

no-triangle hypothesis in a convincing manner.

Could you please provide some references?

Would yould you like that with at symbols or what?

I could give you the references, which you could look up, or I could give you the 200 papers that I have catalogued which are unpublished.

Which is which is what I know of.

Gordon

There are further cancellations at 3 loops and beyond which are not accounted for by the no-triangle hypothesis. These cancellations occur in two and three loops. They are not accounted for by any symmetry and the integral functions are absent and they are many. So the theory is probably secretly hiding a symmetry which noone has encountered before. The theory is probably finite, and if you dont like my comment why dont you ask me or Zvi Bern for details: but they are unproven.