## $T\bar{T}$ in JT Gravity and BF Gauge Theory

Stephen Ebert, Christian Ferko, Hao-Yu Sun, Zhengdi Sun

SciPost Phys. 13, 096 (2022) · published 13 October 2022

- doi: 10.21468/SciPostPhys.13.4.096
- Submissions/Reports

### Abstract

JT gravity has a first-order formulation as a two-dimensional BF theory, which can be viewed as the dimensional reduction of the Chern-Simons description of $3d$ gravity. We consider $T\bar{T}$-type deformations of the $(0+1)$-dimensional dual to this $2d$ BF theory and interpret the deformation as a modification of the BF theory boundary conditions. The fundamental observables in this deformed BF theory, and in its $3d$ Chern-Simons lift, are Wilson lines and loops. In the $3d$ Chern-Simons setting, we study modifications to correlators involving boundary-anchored Wilson lines which are induced by a $T\bar{T}$ deformation on the $2d$ boundary; results are presented at both the classical level (using modified boundary conditions) and the quantum-mechanical level (using conformal perturbation theory). Finally, we calculate the analogous deformed Wilson line correlators in $2d$ BF theory below the Hagedorn temperature where the principal series dominates over the discrete series.

### Cited by 17

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Stephen Ebert, -
^{2}Christian Ferko, -
^{3}Hao-Yu Sun, -
^{4}Zhengdi Sun

^{1}University of California Los Angeles [UCLA]^{2}University of California, Davis [UCD]^{3}The University of Texas at Austin [UT Austin]^{4}University of California, San Diego [UCSD]