$T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS$_3$ gravity

TL;DR

This paper investigates the effects of $Tar{T}$ deformation on chiral bosons and AdS$_3$ gravity, deriving deformed actions, boundary theories, and stress tensors, and confirming consistency with known solutions like BTZ black holes.

Contribution

It provides a comprehensive derivation of the $Tar{T}$ deformed boundary action and stress tensor for AdS$_3$ gravity in Chern-Simons formulation, including all-order deformations for multiple chiral bosons.

Findings

Deformed boundary action matches expectations from $Tar{T}$ flow.

Deformed partition function satisfies the flow equation at one-loop.

Deformed stress tensor aligns with finite cutoff BTZ black hole boundary stress.

Abstract

We study the $T\bar{T}$ deformation of the chiral bosons and show the equivalence between the chiral bosons of opposite chiralities and the scalar fields at the Hamiltonian level under the deformation. We also derive the deformed Lagrangian of more generic theories which contain an arbitrary number of chiral bosons to all orders. By using these results, we derive the $T\bar{T}$ deformed boundary action of the AdS$_3$ gravity theory in the Chern-Simons formulation. We compute the deformed one-loop torus partition function, which satisfies the $T\bar{T}$ flow equation up to the one-loop order. Finally, we calculate the deformed stress tensor of a solution describing a BTZ black hole in the boundary theory, which coincides with the boundary stress tensor derived from the BTZ black hole with a finite cutoff.