Deformations of JT Gravity via Topological Gravity and Applications

TL;DR

This paper explores deformations of Jackiw-Teitelboim (JT) gravity through topological gravity, analyzing their effects on thermal partition functions, phase transitions, and spectral properties, with implications for holography and de Sitter space.

Contribution

It establishes a connection between deformed JT gravity and topological gravity correlators via the KdV hierarchy, providing exact low-temperature partition functions and insights into phase transitions.

Findings

Identifies a Hawking-Page phase transition influenced by defects.

Shows spectral form factors exhibit expected phase transition behavior.

Demonstrates deformations shift the spectral ramp along the real time axis.

Abstract

We study the duality between JT gravity and the double-scaled matrix model including their respective deformations. For these deformed theories we relate the thermal partition function to the generating function of topological gravity correlators that are determined as solutions to the KdV hierarchy. We specialise to those deformations of JT gravity coupled to a gas of defects, which conforms with known results in the literature. We express the (asymptotic) thermal partition functions in a low temperature limit, in which non-perturbative corrections are suppressed and the thermal partition function becomes exact. In this limit we demonstrate that there is a Hawking-Page phase transition between connected and disconnected surfaces for this instance of JT gravity with a transition temperature affected by the presence of defects. Furthermore, the calculated spectral form factors show the qualitative behaviour expected for a Hawking-Page phase transition. The considered deformations cause the ramp to be shifted along the real time axis. Finally, we comment on recent results related to conical Weil-Petersson volumes and the analytic continuation to two-dimensional de Sitter space.