Recent developments on the black hole information paradox have shown that Euclidean wormholes — so called “replica wormholes’’ can dominate the von Neumann entropy as computed by a gravitational path integral, and that inclusion of these wormholes results in a unitary Page curve. This development raises some puzzles from the perspective of factorization, and has raised questions regarding what the gravitational path integral is computing. In this talk, I will focus on understanding the relationship between the gravitational path integral and the partition function via the gravitational free energy (more generally the generating functional). A proper computation of the free energy requires a replica trick distinct from the usual one used to compute the entropy. I will show that in JT gravity there is a regime where the free energy computed without replica wormholes is pathological. Interestingly, the inclusion of replica wormholes is not quite sufficient to resolve the pathology: an alternative analytic continuation is required. I will discuss the implications of this for various interpretations of the gravitational path integral (e.g. as computing an ensemble average) and also mention some parallels with spin glasses.
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Recordings of past talks can be found here: www.youtube.com/channel/UCw9LdPQ5t7Q7muD0qzn70TA