Very Special $T\bar{J}$ deformed CFT

TL;DR

This work introduces a very special class of $T\bar{J}$ deformations in two dimensions that preserve a twisted Lorentz symmetry, yielding a non-unitary yet integrable theory with right-moving Virasoro and left-moving twisted scale symmetry while excluding left-moving Virasoro. The authors develop a general construction based on operator-dependent non-local coordinate changes, enabled by a null current, and provide explicit worldsheet string theory realizations showing how the deformations modify conservation laws without destroying right-moving conformal structure. They further demonstrate equivalence between distinct bc-ghost realizations in flat space and discuss UV improvements due to the underlying $SL(2)$ current algebra. The paper outlines potential holographic embeddings and lattice implementations, framing two complementary interpretations of the deformation and suggesting avenues for extending these ideas to higher dimensions and non-perturbative contexts.

Abstract

We study a very special class of $T\bar{J}$ deformations of conformal field theories in two dimensions. While the deformations break the Lorentz symmetry, they preserve the twisted Lorentz symmetry. The resulting theory has right-moving Virasoro as well as left-moving translation and left-moving (chiral) scale symmetry without left-moving special conformal symmetry (nor left-moving Virasoro symmetry). As in the original $T\bar{J}$ deformations, they may be regarded as an operator dependent non-local change of coordinates. We show concrete examples based on worldsheet string theory and discuss how the non-unitary nature enables us to circumvent various no-go theorems.