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…