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. [please email a.held@imperial.ac.uk for zoom link or password]

I will describe a new procedure for coarse-graining over the gravitational degrees of freedom inside a surface in the context of AdS/CFT. I will prove that in general dimensions, this coarse-graining gives an explanation of an infinite family of gravitational area laws. In three bulk dimensions, it is also straightforward to derive the precise dual of these area laws as strong subadditivity of the von Neuman entropy in the dual CFT. I will discuss a number of implications of this, which include an explanation for the geometric bulk phenomenon of extremal surface barriers