Wednesday, December 04, 2019

Solving information puzzle using replicas

Complexified Euclidean wormholes connecting the replicas save the day

As Yair has pointed out, last week, 5+4=9 quantum gravity big shots who scooped each other – and who were building insights while standing on the shoulders of the remaining 8 replicas that have produced lots of important prerequisites recently – coordinated the publication of two closely related papers
Replica Wormholes and the Entropy of Hawking Radiation (by AHMST, IAS+Ithaca)

Replica wormholes and the black hole interior (by PSSY, Stanford)
where they announced a great new way to look at the black hole interior, derive the black hole entropy, and resolve apparent contradictions related to the information puzzle. This new way involves replicas of black holes – and the exponential factors that are needed to account for the gravitational entropy are obtained from configurations in the path integral of Einstein's gravity in which the replicas are connected by wormholes.

The similarity of the titles and abstracts themselves seems amazing – it seems like circumstantial evidence that these nine physicists' offices are connected by another wormhole (the excessive, "American" capitalization of the 5-author title seems to be the most obvious difference LOL). The basic new ideas are shared by these preprints but they differ in technical aspects that make them rather complementary. The first, 5-author East Coast paper, discusses configurations with Anti De Sitter space connected to the Minkowski space etc. The second, 4-author West Coast paper uses the JT gravity coupled to the SYK model – two toy models that quantum gravity theorists loved to study in recent years.

Note that the small discrepancies have been made logical and the group at Stanford already includes the guy named Stanford, for example. ;-)

It's obvious that I am enthusiastic about this direction of progress. Let's admit that your humble correspondent is a seer who has been forecasting the role for similar tricks at least for 15 years. For example, check the final section of a 2005 text on the Wick rotation and its role in the future of quantum gravity and the information loss paradox or my favorite topology-changing universal derivation of the Bekenstein-Hawking entropy.

OK, the technical details are substantially different in these new papers from the last week, of course, so these guys haven't really plagiarized anything detailed from me. If you don't want to read the 50+76 pages of the preprints, you should start with a 42-minute-long Douglas Stanford's talk at IAS Princeton (that's a place where the group without him works)

that was posted yesterday. Watch also the arguably more entertaining Geoffrey Penington's 38-minute-long sequel about the derivation of the black hole interior from the Hawking radiation – GP is a brilliant boy, indeed. A general lesson which I always expected to be true is that the path integral of Einstein's gravity actually does know about all the aspects of quantum gravity that are universal – such as the universal formulae for the horizon entropy and the universal qualitative lessons about the information loss puzzle. However, to extract the correct lessons, one must use the path integral for quantum gravity properly. And the proper usage involves certain things that are completely absent in the path integral for non-gravitational quantum field theories.

This statement may be formulated in an equivalent, negative way. It's simply wrong to say – as amateur physicists in loop quantum gravities and causal dynamical triangulations etc. naively assume – that the UV physics is absolutely needed to understand the resolution of conceptual, general problems in quantum gravity. A proper analysis of the long-distance physics is enough. Such IR analyses know some of the equivalent information that may also be extracted from the UV methods – and that's a piecewise evidence in favor of the UV-IR connection. This connection is very "stringy" and "non-local" at some level – and it's something that all the amateurs who misunderstand string theory overlook.

What are the main qualitative features of the path integral for quantum gravity relatively to a dull QFT? The main feature is that you can change the spacetime topology in general relativity. So the incorporation of configurations with new topologies – almost equivalently, with wormholes of some generalized types – is actually needed for the path integral for Einstein's theory to be done properly. Maybe you need to add some complexified configurations, too. And when you incorporate these configurations properly, many of the wrong predictions of the "naive quantization of gravity" get fixed.

In both papers, they generate some general formulae for \(n\) replicas of a black hole and then they continue the expressions to the interesting, physical case of \(n=1\) where some of their expressions have a pole. Well, their formulae seem to be valid for complex values of \(n\) while integral but also half-integral values of \(n\) seem to be special. Of course, one may protest against the physical interpretation of the formulae for continuous values of \(n\) but this practice seems normal for good theorists – I think it's on par with the dimensional regularization. Alternatively, you may say that the physics involving a larger number of replicas may be considered "completely physical" and that's where the information puzzles may be resolved without any "faith in the continuation to unphysical values of parameters".

I believe that this precise treatment of the replicas isn't the only way how to apply "similar techniques" – how to show that the proper incorporation of new topologies in the path integral of GR actually makes the theory healthier, not sicker. People need to master many similar things in many other configurations.

Also, I think that the wormholes that come "to the rescue" are morally similar to twisted sectors in string theory. In perturbative string theory, the twisted sectors (and winding strings) are needed to restore the modular invariance (and UV finiteness) of string theory; e.g. in the case of the winding strings, the modular invariance and T-duality are a reflection of the stringy UV-IR connection. I think that these wormholes connecting the replicas of black holes are a "spacetime analogy" of these twisted or wound strings. This is why I think that people should find some more spacetime analogies of the "modular invariance" and other related structures that we know in string theory, too.

Many novel aspects of the stringy world sheet are still waiting to be rediscovered in the quantum gravitational spacetime. Those should include operator product expansions, related algebras, Virasoro-like algebras, minimal and solvable models, critical dimensions determining the right "number of spacetime fields", and more.

Prof Saxana, Harry Potter's grandma, has witchplained some of the tricks from the papers visually.

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