Resurgence in the Virasoro Minimal String and 3d Gravity

TL;DR

This paper develops non-perturbative, resurgent techniques for analyzing the Virasoro minimal string and 3d gravity, revealing new instanton effects, brane phenomena, and eigenvalue density behaviors with implications for black hole physics.

Contribution

It introduces a fully non-perturbative framework for the Virasoro minimal string and 3d gravity using matrix models, including the construction of a non-perturbative partition function and analysis of Stokes transitions.

Findings

Identification of anti-eigenvalues as negative tension D-branes.

Observation of resurgent wall crossing between ZZ- and FZZT-branes.

Connection between eigenvalue density oscillations and black hole onset.

Abstract

We compute non-perturbative, resurgent contributions to the Virasoro minimal string and 3d gravity using techniques from hermitian matrix models. In particular, we construct a fully non-perturbative partition function for the Virasoro minimal string in terms of a Zak transform. In this context, negative tension D-branes appear naturally, which in the matrix model correspond to anti-eigenvalues, or instantons on the involuted sheet of the spectral curve. We further extend this analysis to resolvents and observe resurgent wall crossing phenomena between ZZ- and FZZT-branes. Using recent results that relate the Virasoro minimal string to 3d gravity with end-of-the-world branes we proceed to study the resurgent consequences of summing over the genus in 3d gravity, where we find non-perturbative contributions of doubly exponential type. These statements are then tested using resurgent large-order asymptotics. Lastly, we compute the non-perturbative eigenvalue density for generic hermitian matrix models and identify the change of asymptotic behavior at the edge of the eigenvalue distribution with a Stokes transition. This allows us to identify oscillations in the eigenvalue density with anti-Stokes behavior of FZZT-branes. In the case of 3d gravity with end-of-the-world branes we comment how this Stokes transition coincides with the onset of black hole behaviour and compute the non-perturbative primary density. Furthermore, we apply these techniques to the eigenvalue density of JT gravity to compute higher genus corrections.