JT Gravity Limit of Liouville CFT and Matrix Model

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.

33 pages, 3 figures; v2 minor modifications + references added

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Cited by in corpus (5)

• Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Replica Wormholes from Liouville Theory
• Encoded information of mixed correlations: the views from one dimension higher
• Aspects of Jackiw-Teitelboim Gravity in Anti-de Sitter and de Sitter spacetime