The resurgence of the plateau in supersymmetric ${\cal N}=1$ Jackiw-Teitelboim gravity

TL;DR

This paper analyzes the late-time spectral plateau in supersymmetric ${ m extbf{N}}=1$ Jackiw-Teitelboim gravity, revealing a non-perturbative structure and providing explicit formulas for the ramp-plateau transition.

Contribution

It extends the analysis of spectral form factors to supersymmetric ${ m extbf{N}}=1$ JT gravity, uncovering a truncated genus expansion and deriving exact non-perturbative formulas.

Findings

Perturbative genus sum truncates after one term in the $ au$-scaling limit.

Non-perturbative plateau is derived from properties of the chiral Gaussian ensemble.

Closed-form expression and trans-series expansion for the ramp-plateau transition.

Abstract

Significant progresses have been made recently in understanding the spectral form factor of Jackiw-Teitelboim gravity, particularly at late times where non-perturbative effects are expected to play a dominant role. By focusing on a peculiar regime of large time and fixed temperature, called $\tau$-scaling limit, it was found that it is possible to analytically investigate the late-time plateau directly through the gravitational genus expansion. We extend this analysis to the supersymmetric $\mathcal{N}=1$ generalization of the bosonic theory, revealing an interesting structure. First, we notice that in the $\tau$-scaling limit the perturbative sum over genera truncates after a single term, which solely accounts for the ramp behaviour. Instead a non-perturbative completion, responsible for the plateau, is encoded into an exact formula coming from the properties of the chiral gaussian ensemble, governing the spectral properties of the supersymmetric theory. We are able to recover the non-perturbative contributions by slightly deforming the genus of the involved surfaces and using resurgence theory. We derive a closed-form analytical expression for the late-time plateau and a trans-series expansion that captures the ramp-plateau transition.