A Black Hole Airy Tail
Stefano Antonini, Luca V. Iliesiu, Pratik Rath, Patrick Tran

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…
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