Tuesday, June 27, 2017

Jafferis' and other talks at Strings 2017

Strings 2017 is talking place in Tel Aviv, Israel this week. The talks may be watched at
The Strings 2017 YouTube channel
I hope that the TRF readers will increase the number of views. The most watched video so far has fewer than 140 views, somewhat less than 3 billion views of the Gangnam Style. ;-)

On Wednesday 5 pm, there will be a talk by Andy Strominger and Marika Taylor titled "How you can write a talk promoting feminism, reverse racism, and similar garbage, present it at the annual Strings 2017 conference, and make everyone pretend that everything is alright even though the talk has obviously nothing to do with the topic of the conference". I kindly urge the participants to scream and whistle during the talk if the talk will really take place.

Incidentally, there have been lots of female speakers. Out of the 27 talks I see, at least 5 are female (update: 6 of 29). I am about 90% certain that this overrepresentation of women – almost (update: over) 20% – is due to some design by the organizers. But I've watched all these women's talks (5 times 6 minutes: only short ones) and they mostly seem very smart and competent.

A French TRF reader has chosen the following most interesting talk so far:

It is based on Daniel Jafferis' March 2017 paper. I have just watched it and while it's a little bit more qualitative and a little bit less rich in equations and nice structures than one might want, it's both cool and closely related not only to the questions that I am thinking about but also to many of the answers.

Jafferis gives his own presentation of the reasons why bulk operators in a theory of quantum gravity can't be given by state-independent linear operators. There are numerous examples, some of them were given on this blog, but his simplest one is the "number of components of the spacetime \(N\)". A non-entangled state of two copies of a CFT has the eigenvalue \(N=2\) while the maximally entangled state of the two CFTs – where the entanglement glues the two boundaries – has \(N=1\). Funnily enough, however, these two states (entangled and unentangled) are not orthogonal each other. That contradicts the assumption that \(N\) is a state-dependent Hermitian linear operator on the Hilbert space of the two CFTs. A simple example, indeed.

However, Daniel went further than to just point out that Raju and Papadodimas (and also your humble correspondent, Berenstein, Miller, and others) were right. He made quite some work to demystify the point, too. In particular, he says that the non-existence of similar operators on the CFT(s) space representing the bulk observables isn't any evidence that the AdS/CFT duality breaks down for similar questions. It doesn't break down because the right operator doesn't exist on the bulk side, either. In particular, he argues that the would-be bulk operator isn't physical because it isn't diffeomorphism-invariant, at least not when you allow nonperturbative diffeomorphisms.

To show these points, Jafferis employs some underused yet exciting concept, the Hartle-Hawking wave function, the "initial state of the Universe" calculated with the help of a smooth Euclidean path integral, which solves the Wheeler-DeWitt equation. My understanding is that Daniel only picked the Hartle-Hawking wave function in order to isolate the problem as much as possible – to choose a path integral without any detailed boundary information etc. I am not sure whether he actually claims that there is an interesting and well-defined Hartle-Hawking wave function in examples of AdS/CFT and what predictions it is actually making. He finds that the states \(\ket h\) for some metrics that aren't really orthogonal to each other – a point I made some years ago. Daniel has a new explanation why this overcompleteness of this basis exists: it's because there are many ways to slice a spacetime. I don't quite see that these two effects are "exactly" mapped to each other but maybe Daniel does.

Jafferis also proposes an explanation for the nonperturbatively small overlaps (nonzero inner products). They arise because the complexified geometries may be connected. If I understand well, he says that spacetimes of two different topologies may be considered the same spacetime with different slicings where the difference in slicings is allowed to be complexified. OK, I don't quite understand a single example too well, at the technical level, but I feel that the qualitative statement he makes is true, anyway. In my opinion, one should be more quantitative and careful here because while we "want" to show that some inner products are surprisingly nonzero, there are still lots of inner products that should better still be zero and your cubist treatment of quantum gravity shouldn't invalidate this orthogonality.

The Marolf-Wall paradox disappears because the operators are delegitimized on both sides of the AdS/CFT correspondence. OK, that's a destructive solution to the problem. I would still prefer a solution where fixes are made so that the operators are legitimized on both sides ;-) so that one doesn't throw the baby out with the bath water. To some extent, it seems that Daniel has started to do things like that but it seems very far from a completion. In particular, he made some related steps on a slide he jumped over, one about the local gauge-invariant Hamiltonians that are relational and describe a measurement process. On that slide, he mentions that there's no canonical way to separate the diffeomorphism dressing.

Because, as I mentioned, his solution to the paradox is destructive – he threw away some structures along with the contradictions – he needs a replacement for the delegitimized operators and the physics they used to clarify. So if you agree with his resolution, your new task is to find a framework that describes the outcomes of measurements in the bulk correctly.

Session chair Veronika Hubený asked whether it's right that one can't define a local gauge-invariant operator without specifying a slice. Jafferis basically answers Yes, but the problem only appears at the quantum level when you have to consider wave functions that don't pick a preferred slice – such as the wave functions that are candidates to solve the Wheeler-DeWitt equation. Some geodesics may be used to define something and operators only act as expected if the geodesics go through that slice. I am being vague because I haven't understood his statement at the full precision.

Suvrat Raju tried to rephrase Jafferis' idea about the non-existence of the operator in a slightly different way. He more or less said that there are two ways to quantize observables, through the semiclassical or Hartle-Hawking methods. Jafferis said he would sympathize with the interpretation but this picture is irrelevant here because the semiclassical side quickly runs to spacetime singularities. According to Jafferis, one should therefore be "agnostic" about the existence of the operator in that case. The Jafferis-Raju discussion grew hardcore – I think that fewer than 12 people in the world could follow it – and Veronika Hubený terminated the video by thanks.

A funny terminological detail: I must also praise Daniel for having used the term "ER-EPR correspondence" which I have used at least since July 2013, as an obvious counterpart of the AdS/CFT correspondence. You may check that the first courageous folks have joined me in 2014 but only in recent 2 years, this phrase began to spread. ;-)

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