A quarter-century or so ago, one of common arguments for string theory research was that it was “the only game in town”, in the sense that it was the only possible way to get a unified theory. For instance, back in 1987 David Gross had this to say:
So I think the real reason why people have got attracted to it is because there is no other game in town. All other approaches of constructing grand unified theories, which were more conservative to begin with, and only gradually became more and more radical, have failed, and this game hasn’t failed yet.
As years went on and string theory unification went nowhere, this often was replaced by a new “only game in town” argument, that string theory was the only possible quantum theory of gravity. This argument got strong disagreement from people pursuing Loop Quantum Gravity or any number of other ideas.
This week, Quanta magazine has a new version of the argument, reporting that “Researchers are demonstrating that, in certain contexts, string theory is the only consistent theory of quantum gravity. Might this make it true?” The new argument (based on this and this) seems to be that string theory is the only possible theory of quantum gravity because if you look at a certain class of CFTs (based on orbifolds by permutation groups) and invoke the AdS/CFT conjecture for AdS3/CFT2, the 3d gravity theory in the large N limit would have a density of states more characteristic of string theory than a conventional particle theory.
The most obvious problem here is that it is in 3 space-time dimensions, where there are no physical gravitational degrees of freedom. The S-matrix of quantum gravity is exactly calculable in flat 3d space: it’s zero. There’s a very long history of studying 3d quantum gravity, as a toy model without gravitons, but with just topological degrees of freedom. For more about this, see for instance Steve Carlip’s 1998 book on 3d quantum gravity, which works out a large number of different ways of quantizing 3d gravity (not including string theory). One problem with the argument that string theory is the only way to quantize gravity because it is the only way that works in 3d is that, as Carlip shows, there’s a long list of other completely different ways to do this (all arguably not that relevant to the problem since none have gravitons). This is also quite different than the usual argument that string theory is needed to quantize gravity, which is based on the occurrence of a spin 2 graviton in the spectrum of the string theory.
Ignoring the obvious problem of no gravitons and being in the wrong dimension, there are other problems with the argument, for instance the claim that looking at permutation orbifolds tells you about all CFTs, or the claim that a large density of states at high energy means you have to have a string theory. The article quotes Matt Strassler about this:
But these aren’t really proofs; these are arguments. They are calculations, but there are weasel words in certain places… And just finding a stringy density of states — I don’t know if there’s a proof in that … This is just one property.
Carlo Rovelli sums up the issue with using this to hype string theory and excuse its failures:
They should try to solve the problems of their theory, which are many, instead of trying to score points by preaching around that they are ‘the only game in town.’
I haven’t followed closely work on AdS3/CFT2, but it is a quite interesting topic, although not because it promises a proof of the “universality” of string theory. Chern-Simons theory is based on a very similar relation between a topological 3d qft and 2d CFTs, and there we have some idea what is going on, although many fascinating questions remain. One might hope that AdS3/CFT2 provides a context where one could understand things using some ideas from the Chern-Simons context. This is what Witten did back in 2007 in his paper Three-Dimensional Gravity Revisited (I wrote about this before the paper here). My understanding is that problems with Witten’s proposal later surfaced, I’d be curious to hear from an expert on the latest state of that (perhaps Witten can write a “Three-Dimensional Gravity Revisited Revisited” paper).
There are a lot of wonderful questions still not understood about this story, but I don’t see that using it to argue that string theory is the “only game in town” does anything other than throw one more thing on the pile of outrageous hype generated by string theory partisans over the last 30 years.
Update: There’s been a change to the Quanta article, adding to the quote from Lee Smolin, who is making much the same point I was making in this posting:
“And even in that case [2+1 d], there have existed for a long time counterexamples to the string universality conjecture, in the form of completely worked out formulations of quantum gravity which have nothing to do with string theory.” (String theorists argue that these particular 2+1 gravity theories differ from quantum gravity in the real world in an important way.)
This whole thing really is very strange: on the one hand string theorists are arguing that only string theory can give you quantum gravity, based on an argument in 2+1 d. When you point out to them that there are well-known counterexamples to their argument in 2+1 d, they say “well, things are different in 2+1d than in other dimensions”. Just bizarre…
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