# JT gravity at finite cutoff

### Submission summary

 As Contributors: Jorrit Kruthoff Preprint link: scipost_202006_00046v2 Date accepted: 2020-08-10 Date submitted: 2020-08-04 02:07 Submitted by: Kruthoff, Jorrit Submitted to: SciPost Physics Academic field: Physics Specialties: 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.

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Published as SciPost Phys. 9, 023 (2020)

Dear Editor,

We thank the referees for their comments and questions. We will reply to each referee below.

Report 1:
We thank the referee for her/his kind words and question about holographic entanglement entropy. We are not entirely sure what entanglement entropy is meant here by the referee. In higher dimensions ($d>1$) there is space and one can compute the holographic entanglement entropy of some spatial region. In the bulk (say, for instance AdS$_3$), the EE in TTbar deformed theories then corresponds to the area of an RT surface extending to some finite radial coordinate, which makes it finite. In the present case there is no space or RT surfaces in the bulk and therefore also no holographic entanglement entropy.

Report 2:
We thank the referee for her/his kind words and question. Regarding the Guica/Monten story; in this manuscript we have not attempted to compute the partition function with that definition of the $T\bar{T}$ deformed theory and so we cannot make the comparison in the present work. It would certainly be very interesting to work that out in detail and compare the two prescriptions on a quantum mechanical level.

Report 3:
We thank the referee for her/his kind words and spotting the typo. We have fixed it.

We hope that with this we have answered the questions raised by the referees in a satisfactory manner.

Sincerely yours,

Luca V. Iliesiu, Jorrit Kruthoff, Gustavo J. Turiaci and Herman Verlinde.