Degenerate operators in JT and Liouville (super)gravity

TL;DR

This paper derives explicit expressions for degenerate correlators in JT and supergravity, analyzes their series behavior, proposes higher genus corrections, and explores extensions to super JT models and Liouville supergravity.

Contribution

It provides the first explicit formulas for degenerate Virasoro correlators in JT gravity and extends analysis to supergravity and higher genus corrections.

Findings

Degenerate correlators are structurally simple on the disk.

The 1/C Schwarzian series is asymptotic for generic weights.

JT supergravity saturates the chaos bound at first order.

Abstract

We derive explicit expressions for a specific subclass of Jackiw-Teitelboim (JT) gravity bilocal correlators, corresponding to degenerate Virasoro representations. On the disk, these degenerate correlators are structurally simple, and they allow us to shed light on the 1/C Schwarzian bilocal perturbation series. In particular, we prove that the series is asymptotic for generic weight $h\notin - \mathbb{N}/2$. Inspired by its minimal string ancestor, we propose an expression for higher genus corrections to the degenerate correlators. We discuss the extension to the $\mathcal{N}=1$ super JT model. On the disk, we similarly derive properties of the 1/C super-Schwarzian perturbation series, which we independently develop as well. As a byproduct, it is shown that JT supergravity saturates the chaos bound $\lambda_L = 2\pi/\beta$ at first order in 1/C. We develop the fixed-length amplitudes of Liouville supergravity at the level of the disk partition function, the bulk one-point function and the boundary two-point functions. In particular we compute the minimal superstring fixed length boundary two-point functions, which limit to the super JT degenerate correlators. We give some comments on higher topology at the end.