Jackiw-Teitelboim Gravity, Random Disks of Constant Curvature, Self-Overlapping Curves and Liouville ${\text{CFT}}_1$

Abstract

We propose a microscopic definition of finite cut-off JT quantum gravity on the disk, both in the discretized and in the continuum points of view. The discretized formulation involves a new model of so-called self-overlapping random polygons. The measure is not uniform, implying that the degrees of freedom are not in one-to-one correspondence with the shape of the boundary. The continuum formulation is based on a boundary ${\text{CFT}}_1$ from which we predict some critical exponents of the self-overlapping polygon model. The coupling to an arbitrary bulk matter CFT is also discussed.

14 pages, 1 figure; v2: typos corrected, refs updated; v3: small corrections, published version