JT gravity limit of Liouville CFT and matrix model

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