The Distribution of Ground State Energies in JT Gravity

TL;DR

This paper derives a non-linear differential equation describing the distribution of the lowest energy in JT gravity, revealing universality akin to Tracy-Widom distributions and connecting to phase transitions in matrix models.

Contribution

It introduces a novel ODE approach to characterize the ground state energy distribution in JT gravity, linking it to universality classes and phase transitions in matrix models.

Findings

Distribution matches a non-linear ODE solution

Asymptotic behaviors can be analytically derived

Distribution is analogous to Tracy-Widom for random matrices

Abstract

It is shown that the distribution of the lowest energy eigenvalue of the quantum completions of Jackiw-Teitelboim gravity is completely described by a non-linear ordinary differential equation (ODE) arising from a non-perturbative treatment of a special random Hermitian matrix model. Its solution matches the result recently obtained by computing a Fredholm determinant using quadrature methods. The new ODE approach allows for analytical expressions for the asymptotic behaviour to be extracted. The results are highly analogous to the well-known Tracy-Widom distribution for the lowest eigenvalue of Gaussian random Hermitian matrices, which appears in a very diverse set of physical and mathematical contexts. Similarly, it is expected that the new distribution characterizes a type of universality that can arise in various gravity settings, including black hole physics in various dimensions, and perhaps beyond. It has an association to a special multicritical generalization of the Gross-Witten-Wadia phase transition.