Quantum Gravity Microstates from Fredholm Determinants

TL;DR

This paper explores the microstate structure of two-dimensional Jackiw-Teitelboim quantum gravity using random matrix models and Fredholm determinants, providing explicit non-perturbative insights and numerical results relevant to black hole quantum physics.

Contribution

It introduces a method to extract microstate details of JT gravity via Fredholm determinants and computes the quenched free energy non-perturbatively.

Findings

Explicit kernel for JT gravity models

Numerical construction of energy level statistics

First computation of quenched free energy in this context

Abstract

A large class of two dimensional quantum gravity theories of Jackiw-Teitelboim form have a description in terms of random matrix models. Such models, treated fully non-perturbatively, can give an explicit and tractable description of the underlying ``microstate'' degrees of freedom. They play a prominent role in regimes where the smooth geometrical picture of the physics is inadequate. This is shown using a natural tool for extracting the detailed microstate physics, a Fredholm determinant ${\rm det}(\mathbf{1}{-}\mathbf{ K})$. Its associated kernel $K(E,E^\prime)$ can be defined explicitly for a wide variety of JT gravity theories. To illustrate the methods, the statistics of the first several energy levels of a non-perturbative definition of JT gravity are constructed explicitly using numerical methods, and the full quenched free energy $F_Q(T)$ of the system is computed for the first time. These results are also of relevance to quantum properties of black holes in higher dimensions.