Just got this issue (also linked to from PF home page): http://www.scientificamerican.com/article.cfm?id=search-for-new-physics This whole line of development is unfamiliar to me, and outside of my expertise. The following appear to be some of the papers behind the work described. I am very curious about the opinions of people here on this line of work. http://arxiv.org/abs/hep-th/0702112 http://arxiv.org/abs/0803.1465 http://arxiv.org/abs/0704.2798 http://arxiv.org/abs/hep-th/0610248
Hi PAllen, thanks for posting the links to the earlier Lance Dixon and Zvi Bern articles! We have been hearing about the finiteness of N=8 SUGRA for some time and it is certainly an interesting development. As I recall Lance Dixon gave an Erice summer course on it a few summers back. There may also be video lectures from various conferences. I would welcome any info from the SciAm article you would like to relay. AFAICS the article is behind the paywall---that may change but for now it is freely available only to subscribers. Quote modest excerpts, if you wish, or paraphrase in your own words what you learn from it. My impression is that this is NOT leading to a diff-invariant theory of gravity. Not free of prior geometry, so AFAICS not GR as we know it. But I could be wrong. Others may have more to say about that. So the perturbative finiteness of N=8 Supergravity is very interesting but does not seem to me to obviate the need for a general covariant quantum field theory whose classical limit is GR.
I'll post more after I have read the SiAM article (just glanced at it this morning). However, I have found the following related papers of interest: http://arxiv.org/abs/1004.0476 http://arxiv.org/abs/1005.2703 http://arxiv.org/pdf/1008.2302v1.pdf
Interesting, but the conclusions of the first paper are not really relevant to the SciAm author's hopes: "Here we argue that such a supergravity limit of string theory does not exist in four or more dimensions, irrespective of whether or not the perturbative approximation is free of ultraviolet divergences." As I read it, the whole paper argues against N=8 supergravity as a limite of string theory. The problems described all arise from the starting assumption of "type II superstring theory compactified on a (10 − d)-torus". The author's, at least in this paper, are not making any statements about the viability of N=8 supergravity divorced from any connection to string theory.
Hi Pallen, the information you want exists in a textbook already. In A. Zee's newest edition 'QFT in a Nutshell' he has a chapter on 'Gravity as the square of Yang Mills theory'. This is what they are talking about.
Just to make sure I understand, the SciAm authors are Bern Dixon & Kosower and it is THEY (not the authors of the paper Atyy mentioned) who say "Here we argue that such a supergravity limit of string theory does not exist in four or more dimensions, irrespective of whether or not the perturbative approximation is free of ultraviolet divergences." So the SciAm authors are talking about "the viability of N=8 supergravity divorced from any connection to string theory" But what you are pointing out is that the authors of the paper Atyy mentioned are on a different track where they are NOT talking about the viability of N=8 Sugra divorced from stringy involvements. On rereading, I think what you said actually is quite clear but still want to spell it out to be sure. I hope to get to the library and have a look at the Bern Dixon Kosower article. http://www.scientificamerican.com/article.cfm?id=search-for-new-physics FWIW a recent Bern Dixon et al with some mention of N=8 Sugra and possible areas of overlap (although nominally on another topic, so only tangential) http://arxiv.org/abs/1201.5366
I guess there is the idea that even if all the terms are finite, that isn't sufficient to define a theory, since the series could be divergent. String theory also has series in which all terms are finite, but probably don't form a convergent series. I think the idea is that all the dualities suggest it is part of a well-defined theory. But I guess AdS/CFT is the only part of string theory which has a well-defined suggestion for a non-perturbative definition at the moment? Here's a discussion by Bern "Suppose that N = 8 supergravity turns out to be finite to all orders in perturbation theory. This result still would not prove that it is a consistent theory of quantum gravity at the non-perturbative level. There are at least two reasons to think that it might need a non-perturbative ultraviolet completion ... ... Are there any imaginable pointlike completions for N = 8 supergravity? Maybe the only completion is string theory; or maybe this cannot happen because of the impossibility of decoupling non-perturbative string states not present in N = 8 supergravity." Some people think E7 symmetry is behind Bern's results. Hermann Nicolai wrote a viewpoint about it, and some papers are: http://arxiv.org/abs/1009.1643 http://arxiv.org/abs/1104.5480 This one is funny: "2 years ago, one of the accusers proposed to restore the presumption of innocence".
The SciAm article is about the dramatic simplifications that have occured in the past five years in the structure of scattering amplitudes. In the old days, to compute loop processes in a field theory you had to deal with a proliferation of Feynman diagrams. Even the tree amplitudes with more than 2 incoming, and 2 outgoing particles rapidly produces pages of diagrams that you have to calculate. Some of the authors of the SciAM paper, noticed that they could simplify the calculations by using what are known as unitarity methods. It's entirely equivalent to the old story, it just radically simplifies the solutions. But there were some surprises that came with this. It was quickly noticed that in this new formalism, the structure of the gravity amplitudes look very similar to the structure of something like QCD, but doubled. Technically, if the scattering amplitudes can be put in the form that satisifes what is known as a BCJ duality, then this property holds. Anyway all of this was rigorously proven for string theory and in the context of QFT tree level diagrams, and modern developments have it holding into the loop level. One conjecture has it holding to all loop orders. It is easiest to see in the context of N=8 supergravity, and N=4 SYM, and that is where much of the work is clearest, but it holds in general provided the above condition is satisfied. Further this property and its developments may help elucidate whether or not N=8 Supergravity is perturbatively finite or not (although everyone agrees that it is not consistent at the nonperturbative level as it must be completed to M Theory).
I looked at the library today, but only found the April issue. I take it this is in the May one, already accessible to subscribers online. What especially caught my attention was your phrase about N=8 Sugra viability, which I quote: Zvi Bern and Lance Dixon are two of the top experts in this and much particle theory as well. I see that Kosower is a frequent co-author with them. They are ideal authors for a SciAm piece about N=8 Sugra. And it's fascinating that they split it off from stringy associations and treat it as an independent entity.
Not directly treating Dixon et al's recent work, but provides a useful top level background and context for all this (the latter third of the lecture talks about the "new" approaches to scattering amplitudes): http://media.scgp.stonybrook.edu/video/video.php?f=20120411_2_Arkani-Hamed_qtp.mp4
Thanks, in case anyone wants it here is the arxiv link to the same Zvi Bern, Lance Dixon, et al paper: http://arxiv.org/abs/1103.1848 Amplitudes and Ultraviolet Behavior of N=8 Supergravity Zvi Bern, John Joseph Carrasco, Lance Dixon, Henrik Johansson, Radu Roiban (Submitted on 9 Mar 2011 (v1), last revised 29 Mar 2011 (this version, v2)) In this contribution we describe computational tools that permit the evaluation of multi-loop scattering amplitudes in N=8 supergravity, in terms of amplitudes in N=4 super-Yang-Mills theory. We also discuss the remarkable ultraviolet behavior of N=8 supergravity, which follows from these amplitudes, and is as good as that of N=4 super-Yang-Mills theory through at least four loops. Comments: 28 pages, 8 figures, 3 tables. Talk presented at XVIth European Workshop on String Theory, Madrid, June, 2010 ===quote from introduction=== ... The question we wish to address in this contribution is whether a non-point-like theory is actually necessary for perturbative finiteness. Perhaps with enough symmetry a point-like theory of quantum gravity could have an ultraviolet-finite perturbative expansion. ===
Since the last few posts have been about tracking down references, it might be useful to note http://arxiv.org/abs/arXiv:0704.0777 by Green, Ooguri and Schwarz. This is a useful reference on the nonperturbative inconsistency of maximal sugras that Haelfix is referring to. They explain that the extraction of amplitudes from string theory involves taking a limit where the string coupling [itex]g_s\rightarrow 0[/itex]. The 4d nonperturbative states, which explicitly involve pointlike wound string degrees of freedom, do not decouple at finite string coupling.
Those of you who may know the unitary method: is the essence here that there is some kind of pairwise cancellation of terms at distance if gravity amplitude is depicted as cited above Feynman diagrams are used to calculate outcomes of electro-weak interactions as well, aren't they? What makes QCD diagram structure more suitable for calculating the diagrams for gravity? I read the article, and if I recall it correctly, the authors themselves were still puzzled over the physical implications of this resemblance between doubled QCD and gravity.