A Black Hole Airy Tail

TL;DR

This paper introduces the semi-quenched entropy in JT gravity, a simpler intermediate quantity that maintains positivity and helps analyze black hole ground states using gravitational path integrals.

Contribution

It defines and computes the semi-quenched entropy in JT gravity, bridging bulk and boundary calculations, and clarifies limitations of one-eigenvalue instantons for quenched entropy.

Findings

Semi-quenched entropy has positivity properties of quenched entropy.

Bulk and boundary calculations are consistent in their regime.

One-eigenvalue instantons cannot compute quenched entropy due to saddle-point issues.

Abstract

In Jackiw-Teitelboim (JT) gravity, which is dual to a random matrix ensemble, the annealed entropy differs from the quenched entropy at low temperatures and goes negative. However, computing the quenched entropy in JT gravity requires a replica limit that is poorly understood. To circumvent this, we define an intermediate quantity called the semi-quenched entropy, which has the positivity properties of the quenched entropy, while requiring a much simpler replica trick. We compute this in JT gravity in different regimes using i) a bulk calculation involving wormholes corresponding to the Airy limit of the dual matrix integral and ii) a boundary calculation involving one-eigenvalue instanton saddles proposed by Hern\'andez-Cuenca, demonstrating consistency between these two calculations in their common regime of validity. We also clarify why similar one-eigenvalue instanton saddles cannot be used to compute the quenched entropy due to a breakdown of the saddle-point approximation for the one-eigenvalue instanton in the replica limit. Our results show how to use the gravitational path integral to prove that black holes in JT gravity have isolated ground states and to study their properties.