A Black Hole Airy Tail: Part 1

Part 1: In this talk, I will discuss an entropic puzzle in JT gravity and its resolution, which requires taking into account non-perturbative effects in the gravitational path integral. In JT gravity, which is dual to a random matrix ensemble, the gravitational thermal entropy becomes negative at very low temperatures. This puzzle arises when computing the annealed (instead of quenched) entropy, corresponding to an incorrect averaging procedure in the dual matrix model. We define an “intermediate” quantity, the semi-quenched entropy, to show how the positivity of the quenched entropy can be rescued. From the bulk perspective, both a resummation of higher-genus topologies and wormhole effects are crucial. From the matrix model perspective, the resolution relies on the statistics of eigenvalues near the edge, governed, in different regimes, by the Airy distribution or by 1-eigenvalue instantons. A more general version of this puzzle and its resolution will be discussed by Stefano Antonini in Part 2 of this talk.