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

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