Solving a family of $T\bar{T}$-like theories

TL;DR

This paper generalizes the $Tar{T}$ deformation to a broader class of 2D quantum field theories, deriving and solving transport equations for energy levels and charges, and validating results with AdS/CFT correspondence.

Contribution

It introduces a generalized deformation framework for 2D QFTs involving antisymmetric conserved current combinations, extending the $Tar{T}$ paradigm and solving related transport equations.

Findings

Derived transport equations for deformed energy levels.

Solved for theories with flavor currents and stress tensor.

Validated results with AdS/CFT correspondence.

Abstract

We deform two-dimensional quantum field theories by antisymmetric combinations of their conserved currents that generalize Smirnov and Zamolodchikov's $T\bar{T}$ deformation. We obtain that energy levels on a circle obey a transport equation analogous to the Burgers equation found in the $T\bar{T}$ case. This equation relates charges at any value of the deformation parameter to charges in the presence of a (generalized) Wilson line. We determine the initial data and solve the transport equations for antisymmetric combinations of flavor symmetry currents and the stress tensor starting from conformal field theories. Among the theories we solve is a conformal field theory deformed by $J\bar{T}$ and $T\bar{T}$ simultaneously. We check our answer against results from AdS/CFT.