Conserved currents and $\text{T}\bar{\text{T}}_s$ irrelevant deformations of 2D integrable field theories

TL;DR

This work broadens the landscape of solvable irrelevant deformations in 2D QFTs by introducing geometrical deformations built from higher-spin conserved currents, ${\bf T}_{\mathbf s+1}$, yielding Lorentz-violating, ${\bf T}\bar{\text{T}}_{\mathbf s}$-type theories that connect with ${\rm J}\bar{\rm T}$-like models. The authors develop a general framework based on field-dependent coordinate changes that maps undeformed currents to deformed ones via closed 1-forms, enabling construction of the full tower of deformed integrals of motion. They provide explicit quantum realizations using the massless free boson and the sine-Gordon model, deriving generalized Burgers-type evolution equations for the spectrum and identifying the corresponding scattering phase factors that encode the deformations in the NLIE/Bethe-Ansatz formalism. In the ${\bf s}\to 0$ limit, the analysis naturally yields ${\rm J}\bar{\rm T}$-type structures, including a four-parameter deformation family and Legendre-transformed Hamiltonians, illustrating a unified gravity-like and integrable description of these non-Lorentz-invariant perturbations. The results establish a coherent classical-quantum dictionary for geometrical TT_s deformations and point to rich connections with holography, nonlocal charges, and generalized gravity-like theories in two dimensions.

Abstract

It has been recently discovered that the $\text{T}\bar{\text{T}}$ deformation is closely-related to Jackiw-Teitelboim gravity. At classical level, the introduction of this perturbation induces an interaction between the stress-energy tensor and space-time and the deformed EoMs can be mapped, through a field-dependent change of coordinates, onto the corresponding undeformed ones. The effect of this perturbation on the quantum spectrum is non-perturbatively described by an inhomogeneous Burgers equation. In this paper, we point out that there exist infinite families of models where the geometry couples instead to generic combinations of local conserved currents labelled by the Lorentz spin. In spirit, these generalisations are similar to the $\text{J}\bar{\text{T}}$ model as the resulting theories and the corresponding scattering phase factors are not Lorentz invariant. The link with the $\text{J}\bar{\text{T}}$ model is discussed in detail. While the classical setup described here is very general, we shall use the sine-Gordon model and its CFT limit as explanatory quantum examples. Most of the final equations and considerations are, however, of broader validity or easily generalisable to more complicated systems.