# JT gravity at finite cutoff

### Submission summary

 As Contributors: Jorrit Kruthoff Preprint link: scipost_202006_00046v1 Date submitted: 2020-06-15 Submitted by: Kruthoff, Jorrit Submitted to: SciPost Physics Discipline: Physics Subject area: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We compute the partition function of 2D Jackiw-Teitelboim (JT) gravity at finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt wavefunctional in radial quantization and (ii) through a direct computation of the Euclidean path integral. Both methods deal with Dirichlet boundary conditions for the metric and the dilaton. In the first approach, the radial wavefunctionals are found by reducing the constraint equations to two first order functional derivative equations that can be solved exactly, including factor ordering. In the second approach we perform the path integral exactly when summing over surfaces with disk topology, to all orders in perturbation theory in the cutoff. Both results precisely match the recently derived partition function in the Schwarzian theory deformed by an operator analogous to the $T\overline{T}$ deformation in 2D CFTs. This equality can be seen as concrete evidence for the proposed holographic interpretation of the $T\overline{T}$ deformation as the movement of the AdS boundary to a finite radial distance in the bulk.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission scipost_202006_00046v1 on 15 June 2020

## Reports on this Submission

### Report

This is a remarkable paper addressing issues about imposing a finite-cutoff in the JT gravity in a finite-cutoff setup. They compare the methods from the evaluation of the Wheeler-DeWitt functional and the gravitational path integral in the bulk, obtaining agreement in the boundary.

This paper illustrates new perspectives among JT gravity, TTbar deformation, and the information paradox setup discussed recently in the high energy theory community.

A particularly important problem related to this story, and I am particularly interested in is the possible finiteness of entanglement entropy in the holographic cutoff AdS in higher dimensions. The problem appears in higher dimensions, but I am curious if this also emerges in this 1+1 dimensional bulk, and I believe that this might also be related to the information problem in the setup of JT gravity. I look forward to the authors' comments on it.

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