JT gravity as a matrix integral

TL;DR

This paper establishes a precise connection between JT gravity partition functions on arbitrary surfaces and a specific matrix integral, revealing a nonperturbative completion linked to D-brane-like effects in spacetime.

Contribution

It demonstrates that JT gravity's partition functions correspond to a matrix integral's genus expansion, with a mapping from Mirzakhani's recursion to topological recursion, providing a nonperturbative framework.

Findings

Partition functions match a matrix integral's genus expansion.

Mirzakhani's recursion maps onto topological recursion.

Nonperturbative effects resemble D-brane contributions.

Abstract

We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The boundaries are of the type relevant in the NAdS${}_2$/NCFT${}_1$ correspondence. We show that the partition functions correspond to the genus expansion of a certain matrix integral. A key fact is that Mirzakhani's recursion relation for Weil-Petersson volumes maps directly onto the Eynard-Orantin "topological recursion" formulation of the loop equations for this matrix integral. The matrix integral provides a (non-unique) nonperturbative completion of the genus expansion, sensitive to the underlying discreteness of the matrix eigenvalues. In matrix integral descriptions of noncritical strings, such effects are due to an infinite number of disconnected worldsheets connected to D-branes. In JT gravity, these effects can be reproduced by a sum over an infinite number of disconnected geometries -- a type of D-brane logic applied to spacetime.