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

TL;DR

This paper explores how $T\bar{T}$-type deformations affect JT gravity formulated as a 2D BF theory, analyzing boundary conditions, Wilson line observables, and correlators at classical and quantum levels, including in 3D Chern-Simons and 2D regimes.

Contribution

It provides a novel interpretation of $T\bar{T}$ deformations as boundary condition modifications in BF and Chern-Simons theories, with detailed analysis of Wilson line correlators.

Findings

Deformation modifies boundary conditions in BF and Chern-Simons theories.

Wilson line correlators are affected by $T\bar{T}$ deformation at classical and quantum levels.

Results include explicit calculations of deformed correlators below the Hagedorn temperature.

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.