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arXiv · 2108.12096

JT Gravity Limit of Liouville CFT and Matrix Model

Kenta Suzuki·Tadashi Takayanagi
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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.

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Kenta Suzuki, Tadashi Takayanagi. 2021-08-27. JT Gravity Limit of Liouville CFT and Matrix Model. https://doi.org/10.1007/jhep11(2021)137

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