Non-perturbative effects in JT gravity from KdV equations

TL;DR

This paper explores non-perturbative effects in JT gravity by solving KdV equations with transseries, providing explicit solutions and confirming results through topological recursion in random matrix models.

Contribution

It introduces a systematic method to construct transseries solutions to the KdV equation relevant for JT gravity, extending the understanding of non-perturbative effects.

Findings

Transseries solutions to the KdV equation for JT gravity are explicitly constructed.

Leading non-perturbative sector results match topological recursion calculations.

The approach connects topological gravity with non-perturbative analysis in JT gravity.

Abstract

It is well-known that the partition function of the Jackiw-Teitelboim (JT) gravity is obtained by an integral transformation of volumes of moduli spaces for Riemann surfaces, also known as the Weil-Petersson volumes. This fact enables us to compute the perturbative genus expansion of the partition function by solving a KdV-type non-linear partial differential equation. In this work, we find that this KdV equation also admits transseries solutions. We give a systematic algorithm to explicitly construct a one-parameter transseries solution to the KdV equation. Our approach is based on general two-dimensional topological gravity, and the results for the JT gravity are easily obtained as a special case. The results in the leading non-perturbative sector perfectly agree with another independent calculation from topological recursions in random matrices.