Flow equations for generalised $T\bar{T}$ deformations

TL;DR

This paper develops a comprehensive framework for integrable deformations of 2D quantum field theories extending the $T\bar{T}$ deformation, deriving flow equations for higher-spin charges using a generalized Gibbs ensemble.

Contribution

It introduces the most general class of integrable deformations related to higher-spin charges and derives their flow equations, generalizing known results.

Findings

Derived a general flow equation for higher-spin charges under deformations.

Reproduced known flow equations as special cases.

Provided a new perspective on integrable deformations via CDD factors.

Abstract

We consider the most general set of integrable deformations extending the $T\bar{T}$ deformation of two-dimensional relativistic QFTs. They are CDD deformations of the theory's factorised S-matrix related to the higher-spin conserved charges. Using a mirror version of the generalised Gibbs ensemble, we write down the finite-volume expectation value of the higher-spin charges, and derive a generalised flow equation that every charge must obey under a generalised $T\bar{T}$ deformation. This also reproduces the known flow equations on the nose.