A successful test in \(AdS_3\)
The first hep-th paper today is
Serin Hall, Rutgers University, NJ
We sometimes say that string theory is the only consistent theory of quantum gravity. It's the only game in town. This is an observation mostly based on various types of circumstantial evidence. Whenever you try something that deviates from string/M-theory, you run into inconsistencies. Sometimes you don't run into inconsistencies but something else happens. Many good ideas that were thought to be "competitors" to string theory were shown to be just aspects of some (usually special) solutions to string theory (noncommutative geometry, CFT, matrix models, and even the Hořava-Lifshitz class of theories have been found to be parts of string theory), and so on. And decades of attempts to find a truly inequivalent competing theory have utterly failed. That's not a complete proof of their absence, either, but it is evidence that shouldn't be completely ignored.
But that doesn't mean that the statement that every consistent theory of quantum gravity has to be nothing else than another approach to string/M-theory is just an expression of vague feelings, a guesswork, or a partial wishful thinking. We don't have the "most complete proof" of this assertion yet – this fact may be partly blamed on the absence of the completely universal, most rigorous definition of both "quantum gravity" and "string theory". But there exist partial proofs and this paper is an example.
These three guys look at a specialized version of the claim that "string theory is the only game in town", namely at
string theory is the only game in the \(AdS_3\) neighborhood of the town.It's not quite the same but you know, if there were other games (and especially if there were numerous games) in the other neighborhoods aside from \(AdS_3\), it would be very likely that there is a non-stringy game in the \(AdS_3\) neighborhood, too.
If the asymptotic conditions are \(AdS_3\), the isometries coincide with the conformal group of the two-dimensional conformal field theory, \(CFT_2\). This boundary \(CFT_2\) should be sort of local, due to the large proper distances near the \(AdS_3\) boundary. By these comments, I only want to make you accept that it is reasonable to pick boundary \(CFT_2\) theories as a representative of the quantum gravity theories in \(AdS_3\).
These \(CFT_2\) theories are not quite guaranteed to arise from string theory, despite the fact that \(AdS/CFT\) is a paradigm shift that resulted from string theory.
The three physicists investigate \(CFT_2\) theories that are orbifolds by permutation groups and see that only some of them admit a large \(N\) limit. Those that admit the large \(N\) limit allow you to make the dual \(AdS_3\) space large in the Planck units (and therefore just mildly curved). And after some playing with weights, the twisted and untwisted partition functions, and the Cardy formula for the density of states that string theorists know and love, the three men show that these \(CFT_2\) theories always reproduce the Hagedorn – string-theory-derived – density of the states at high energies.
They proceed in "a class after another class" way but I feel that there may exist a more direct proof that derives the existence of a small string coupling from the large value of \(N\), and therefore establishes some weakly coupled strings. But I don't quite know how to complete this shorter proof. At any rate, it is right for them to pick the main corollary of the work:
This is evidence that, within this landscape [of permutation orbifolds, \(CFT_2\) theories], every theory of quantum gravity with a semi-classical limit is a string theory.Some people like to say that they disagree with this statement. But instead of providing us with papers that actually analyze technical properties of some classes of theories – and their existing or non-existing links with string/M-theory – they think that quotes of philosophers (ideally Popper) and loud demagogic screaming is enough to counterbalance actual papers such as the papers by Belin et al.
Well, it's not enough. Whether a theory with certain properties and making certain predictions exists is a mathematical question and if you haven't mastered the relevant mathematics, you should use the excellent opportunity to shut up. The evidence gives us very good reasons to think that string theory is the only game in town and those who scream that this mustn't be the case are just deluded populist scumbags without any valuable content.
And that's the memo.
Bonus: this January 2012 Michio Kaku video is called "String Theory Is the Only Game In Town" (which is why it's here) but (aside from his slightly annoying obsession with the media and press releases) he said many things about the ugliness of the Standard Model, the dark matter, and the Higgs boson, too. Note that it was half a year before the Higgs boson discovery was announced. But he correctly predicted that the room for the Higgs had been narrowed down and sometime in 2012 – and yes, it was almost exactly in the middle of the year – the particle would be found and the champagne bottles would pop open (correct prediction, too). I was sanely predicting the same obvious thing but many physicists were surprisingly clueless about the "coming Higgs events".