Resurgent Asymptotics of Jackiw-Teitelboim Gravity and the Nonperturbative Topological Recursion

TL;DR

This paper explores the nonperturbative resurgent properties of Jackiw-Teitelboim gravity by developing instanton calculus and extending topological recursion, revealing new insights into the large-genus behavior of Weil-Petersson volumes.

Contribution

It introduces a nonperturbative extension of topological recursion and applies it to analyze instanton sectors in Jackiw-Teitelboim gravity, advancing understanding of its resurgent structure.

Findings

Validated the resurgent nature of the perturbative series in JT gravity.

Identified the necessity of ZZ and FZZT effects for resurgence.

Derived new resurgence formulas for Weil-Petersson volumes growth.

Abstract

Jackiw-Teitelboim dilaton-quantum-gravity localizes on a double-scaled random-matrix model, whose perturbative free energy is an asymptotic series. Understanding the resurgent properties of this asymptotic series, including its completion into a full transseries, requires understanding the nonperturbative instanton sectors of the matrix model for Jackiw-Teitelboim gravity. The present work addresses this question by setting-up instanton calculus associated to eigenvalue tunneling (or ZZ-brane contributions), directly in the matrix model. In order to systematize such calculations, a nonperturbative extension of the topological recursion formalism is required -- which is herein both constructed and applied to the present problem. Large-order tests of the perturbative genus expansion validate the resurgent nature of Jackiw-Teitelboim gravity, both for its free energy and for its (multi-resolvent) correlation functions. Both ZZ and FZZT nonperturbative effects are required by resurgence, and they further display resonance upon the Borel plane. Finally, the resurgence properties of the multi-resolvent correlation functions yield new and improved resurgence formulae for the large-genus growth of Weil-Petersson volumes.