Wednesday, December 24, 2014

Every theory of quantum gravity is a part of string theory: a partial proof

A successful test in \(AdS_3\)

The first hep-th paper today is
String Universality for Permutation Orbifolds
by Alexandre Belin, Christoph A. Keller, and Alexander Maloney who are at McGill and Rutgers University, my graduate Alma Mater (I know A.M. from Harvard). Note that Christopher was terrified by the disagreement between the other two authors when it comes to "-re" or "-er" in their first name, so he erased it from his name altogether. ;-)

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".


  1. Really interesting work indeed! Just wanted to point out that there was another paper on the topic a couple of weeks ago

    Happy holidays!

  2. Very cute, just from reading this blog post (and the abstract) I like and admire this very clear cut reasoning and line of thought (certain things are slightly familiar to me from what I have see in the First Course of ST, should reconsider that) those physicists apply to attack to proof that ST is the only game in town in this specific case :-)

    This is how good physics works, and not by slinging slogans, mud, and what else around ...

    Cheers to them for their cool work and happy Christmas to everybody :-)

  3. Jingle strings, jingle strings, jingle all the way.
    Milgrom is the cosmological Kepler of our day.

  4. I am thinking of that song "Video killed the radio star" : "Mathematicians killed the theorectical physicists. " It's no coincidence that Witten has a fields medal.

  5. Dilaton: Just want to add a Merry Christmas to you from Boo and me.

  6. "Mathematicians" gave the birth to theoretical physics (like Newton) and were running it ever since.

    Incidentally, Witten is a theoretical physicist: the adjective is derived from the world "theory". Theorectical physicists are completely different physicists – I could name many of them – who study God's rectum.

  7. What is not understood about string theory that prevents physicists from writing down an explicit, complete theory of quantum gravity? Perhaps physicists don't know what's missing (likely), but can you make a guess?

  8. kashyap vasavadaDec 24, 2014, 5:56:00 PM

    It is great to know that the only game in town (ST) is consistent with standard model and quantum gravity. Hopefully, one of these days it will be able to predict all these dozens of parameters of standard model .

  9. Lubos, if GR is in fact perturbatively nonrenormalizable but nonperturbatively renormalizable (in a similar spirit of, as Reuter used to suggest recently ( what would be the implications for Stringy descriptions of QG? Merry Christmas!

  10. I think we are witnessing the birth of the new term, to be used widely hereupon.

  11. The two Alexes are from McGill, not Rutgers

  12. Aleksandar MikovicDec 25, 2014, 10:15:00 AM

    The problem with the statement that any d-dimensional QG theory with a good SC limit is a string theory on AdS(d) is that it does not apply to the case when the topology of the spacetime is S x R, where S (the space) is compact. In the AdS string theory case, the topology of the spacetime requires S to be non-compact, so that at asymptotic infinity one has the CFT(d-1) group of symmetries.

  13. Aleksandar MikovicDec 25, 2014, 12:52:00 PM

    String theory is not the only game in town as far as the quantum gravity is concerned, since in arxiv:1407.1124, 1402.4672 and 1302.5564 has been demonstrated that there is a well-defined QG theory which has a good semiclassical limit.
    This QG theory is a Regge path-integral formulation, which is based on the assumption that the spacetime is a PL manifold corresponding to a triangulation of a smooth 4d manifold, so that the spacetime triangulation is physical. For triangulations with a large number of 4-simplexes, the Regge QG can be approximated by the usual QFT with a physical cutoff given by the minimal edge length in the triangulation.