Degenerate operators in JT and Liouville (super)gravity

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.

89 pages, v3: included appendix A.2 on degenerate crossing, rearranged and augmented sections to improve readability, added references, matches published version

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• A JT supergravity as a double-cut matrix model
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Microstructure in matrix elements
• Phase transitions for deformations of JT supergravity and matrix models
• Gravity without averaging
• Quantum group origins of edge states in double-scaled SYK
• Boundary correlators and the Schwarzian mode
• Boundary Conditions for $\mathrm{Ad}{\mathrm{S}}_2$ Dilaton Gravity
• Target space diffeomorphisms in Poisson sigma models and asymptotic symmetries in 2D dilaton gravities