The highlighted article in Friday's Physical Review Letters is something Peter Woit has been going on about for months: "Cancellations Beyond Finiteness in N=8 Supergravity at Three Loops". It's been on the ArXiv for ages, but I'm old school, and don't think of papers as real until they're actually released in peer-reviewed journals.
The thing is, I'm really not sure what this means. That is, I know what the paper is about, but I'm not sure what the implications are.
My extremely limited understanding is that "N=8 supergraviy" is one of the early attempts at creating a theory of quantum gravity that would unify it with the other fundamental forces. It was a hot topic for a while some years back, but it turned out to be fiendishly difficult to do any calculations with it, and there were some things about it that made people think the theory wasn't mathematically consistent-- that is, when you added up all the contributions of all the interactions that could possibly occur, you wouldn't get a finite answer. The apparent inability of these theories to generate finite results led to their general abandonment, and is one of the steps along the road to the current dominance of string theory.
The gist of the paper appears to be that if you actually sit down and grind through the fiendishly difficult calculations needed to do anything with the theory, it turns out that it actually does give finite answers, at a point where it had been suspected that the theory would diverge. This is apparently due to the cancellation of some terms in the equations that don't necessarily look like they'll cancel out. It's not clear that this will work at higher orders, but it may well turn out to be a theory that gives reasonable answers after all.
The question is, what does that mean? If it's actually a finite theory, does this mean it was abandoned in error, or are there other problems with the method that would still rule it out as a solution to the problem of quantum gravity? It was obviously considered promising at one time, but do those reasons still apply?
Answers from people other than Peter Woit would be much appreciated, though Peter is obviously welcome to weigh in-- it's just that much of the little I know of the subject is drawn from Not Even Wrong, so I'd like to hear a different take...
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Supergravity theories were once a shining hope for quantum gravity, but less supersymmetric theories turned out not to be finite, which encouraged people to move on to superstring theory.
If N=8, d=4 is perturbatively finite, that would be interesting since it contradicts string theory lore that you can't have a consistent theory of quantum gravity in 4D based around a theory of point particles. But it wouldn't be as interesting as it once would have been, because it's been pretty well shown by now that the theory is nonperturbatively related to M theory. In other words, whether it's finite or not, it's still a part of the whole string theory program, and does not stand alone as a competing theory of quantum gravity.
You could read what Lubos has to say on the matter. (There are some loopholes in the argument I've presented; you have to assume that the nonperturbative completion of supergravity is unique to imply string theory from supergravity.)
I'm far from an expert on this sort of thing, but the whole thing seems a bit puzzling. The not at all clear (to me, at least) that the sort of miraculous cancellations that may render the theory perturbatively finite would survive the addition of all the crap that would be necessary to get something resembling the real world out of it.
The relation to string theory is a bit odd, too. Pure N=8 SUGRA does not seem to arise as a limit of string theory -- there's always some other junk floating around. On the other hand, even if you didn't know about string theory, there'd be reason to suspect that that nonperturbative junk is hiding in the theory just from studying the solutions to the supergravity. Thus, you might make the argument that the finiteness of the preturbation expansion is only interesting for perturbation theory, but that when you try to do stuff nonperturbatively, all this other junk essentially forces you to do string/M-theory.
Supergravity was pursued as a theory of quantum gravity back in the 80s, starting just before the modern version of string theory. One of the attractions of the maximally supersymmetric (N=8) version is that it was thought to be finite. However, the consensus after a few years was that this is incorrect, that a divergence must occur at some high order in perturbation theory. That would mean that the theory needs to be renormalized, so it is only an effective field theory which will have to be subsumed by something else, maybe string theory, maybe something else. There were other issues as well- because of the high degree of symmetry it could not have structure needed for particle physics (spontaneous breaking of SUSY, chiral fermions, realistic gauge groups,...).
Nevertheless, nobody ever calculated the expected divergence, until recently the calculation was intractable. Now, with advances to do with twistor techniques, there are some indications the expcted divergence is not there after all, which leads people to conjecture that the theory may be finite after all. This is fascinating technically- unexpected cancellations indicate some symmetry lurking in the background, and this would advance our understanding of supersymmetric field theories in general, for example further relate them to the twistor program of Penrose.
The relation of all this to string theory is peripheral at best. Making this into a "debate" is certainly not going to serve the interests of clarity...
Personally, I'm very much enamoured of the idea that d=4 N=8 supergravity might be perturbatively finite.
If true, then the full M-theory on T^7 would emerge, nonperturbatively from that ostensibly 4-dimensional theory.
Whether there are other possible nonperturbative quantum theories of d=4 N=8 supergravity is interesting to speculate about.
But it may simply be that the theory is not perturbatively renormalizable (let alone finite), and must be UV-completed to the full string theory.
No one knows, but aside from the exotic possibility that N=2 SUGRA is finite and admits a non-minimal choice of Dirac-quantization condition, there's no "new" physics here. At least, none that would be of the slightest interest to all but a handful of specialists...
One more word about the implications, elaborating on my previous comment. The way I read it the main interest in the result is not so much the question of the N=8 SUGRA theory itself, as I said it has other problems as a realistic theory of particle physics.
Rather, the main interest in my mind is that the cancellations needed to obtain a finite result do not currently have any explanation as a result of any symmetry of the theory. This suggests that the N=8 theory (and maybe similar field theories) has vastly more symmetries than what is manifest in the current way of doing calculations. Figuring out the details may have implications that go well beyond the N=8 theory itself. Then again, it may not, nobody knows...
You could read what Lubos has to say on the matter.
I could, but his manifest craziness on, well, everything else is a little off-putting.
I'm uncertain of the meaning of phrases like "nonperturbatively related to M-theory," as well, but I need to think about how to phrase that question. And, really, it's beyond my ability before seven in the morning.
I think Moshe makes the most important point: it looks like N=8 SUGRA has structure we don't understand, structure that makes its high-energy behavior much better than expected. There are well-known problems with using N=8 SUGRA itself to build a unified theory, but the fact that this kind of finiteness is possible at all in a QFT is remarkable and unexpected. If one could understand what is causing it, it is reasonable to expect that other QFTs may exist that share this better high-energy behavior.
The "move along, nothing to see here, this is only interesting to experts" line you are getting from some string theory partisans is kind of laughable. This is the most interesting development in the field of quantum gravity in quite a few years. It also falsifies the main argument that is often used to justify string theory, that perturbatively, QFTs involving gravity are inherently ill-behaved.
The situation now may be much like what happened back in 1973 with asymptotic freedom. At the time, the ideology was that QFTs were inherently ill-behaved at high energy, and needed to be replaced by S-matrix theory or string theory, or something else. The (difficult for the time) calculation of the beta-function by Gross-Politzer-Wilczek showed that this expectation was wrong. In that case, because of the existence of a lot of experimental data that could be used to identify the right gauge theory of the strong interaction, connection to experiment was quickly made. That's not likely to happen in this case, but in the long term, this realization that a certain QFT for gravity does make sense perturbatively may very well be a turning point for the whole subject.
The claim of Lubos et. al. (the information in his posting is more lucid than usual, but the conclusions he draws are based on the usual ideological fanaticism) that since there is a conjectured connection between a non-perturbative version of N=8 supergravity and string theory, N=8 supergravity can't be understood non-perturbatively without string theory doesn't hold much if any water. For string theorists to be attacking a theory as not interesting in itself because, while it makes sense perturbatively, it has not yet been understood and shown to be consistent non-perturbatively, is kind of amusing to watch.
There's a missing sentence in my post above, I just noticed -- it should say after the first sentence that N=8 SUGRA is very far from the real world, and that it needs a lot of changes to even come close to resembling it.
Chad, even if N=8 is finite, there is an independent question to ask, that of unitarity, which is what is referred to by the cryptic sentence you quoted. There are some string theories that include N=8 SUGRA, but also have other things as well. If there is finite probability for the N=8 states to transform to the extra states in those string theories, the N=8 by itself is incomplete (non-unitary). Maybe there is more than one completion of the N=8 theory, but there is an obvious one- the aforementioned string theory.
But, as I said above, the stringy angle on this is a little forced. If the conjecture is true (there is not a lot of evidence right now...) I'm sure we'll learn interesting things about field theory and string theory both, after all the two subjects are not unrelated...