Low-temperature entropy in JT gravity

TL;DR

This paper investigates the low-temperature entropy behavior in Jackiw-Teitelboim (JT) gravity, linking it to random matrix ensembles and calculating the entropy coefficient using universal eigenvalue distribution results.

Contribution

It derives the low-temperature entropy scaling in JT gravity by connecting it to Dyson and Altland-Zirnbauer ensembles, providing explicit calculations of the entropy coefficient.

Findings

Low-temperature entropy in JT gravity scales as T^{eta+1}.

The entropy coefficient is computed using eigenvalue distribution universality.

Corrections to the coefficient are doubly exponentially small in S_0.

Abstract

For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with $\beta \in \{1,2,4\}$, the low-temperature mean entropy can be shown to vanish as $\langle S(T)\rangle\sim \kappa T^{\beta+1}$. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a $\beta =2$ ensemble, with a classical eigenvalue density $\propto e^{S_0}\sqrt{E}$ when $0 < E \ll 1$. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate $\kappa$ up to corrections that we argue are doubly exponentially small in $S_0$.