JT Gravity Limit of Liouville CFT and Matrix Model

TL;DR

This paper establishes a detailed correspondence between JT gravity in AdS2, a specific two-dimensional string theory involving Liouville CFTs, and a matrix model dual, also extending to dS2, revealing deep connections between gravity, string theory, and matrix models.

Contribution

It demonstrates a precise equivalence between JT gravity and a semiclassical limit of c<1 string theory involving Liouville CFTs, and identifies a matrix model dual for this setup.

Findings

Matching of actions, partition functions, and amplitudes between JT gravity and Liouville CFTs

Reproduction of boundary Schwarzian theory from Liouville theory

Identification of a matrix model dual with a specific time-dependent background

Abstract

In this paper we study a connection between Jackiw-Teitelboim (JT) gravity on two-dimensional anti de-Sitter spaces and a semiclassical limit of $c<1$ two-dimensional string theory. The world-sheet theory of the latter consists of a space-like Liouville CFT coupled to a non-rational CFT defined by a time-like Liouville CFT. We show that their actions, disk partition functions and annulus amplitudes perfectly agree with each other, where the presence of boundary terms plays a crucial role. We also reproduce the boundary Schwarzian theory from the Liouville theory description. Then, we identify a matrix model dual of our two-dimensional string theory with a specific time-dependent background in $c=1$ matrix quantum mechanics. Finally, we also explain the corresponding relation for the two-dimensional de-Sitter JT gravity.