An integrable Lorentz-breaking deformation of two-dimensional CFTs

TL;DR

This paper introduces a universal, integrable Lorentz-breaking deformation of 2D CFTs with a conserved $U(1)$ current, defined by $\mathcal{O}_{J\bar{T}}= J \bar{T}-\bar{J}\Theta$, and derives the exact finite-size spectrum and thermodynamics for purely holomorphic or antiholomorphic currents. The holomorphic case yields nontrivial shifts in the spectrum, with $E^R(\mu,R)=E^R(0,R-\mu Q)$ and a deformation of $E^L$, while the antiholomorphic case leaves the spectrum undeformed; thermodynamics exhibits a Cardy-like entropy and a divergence as the circle size approaches $R=\mu Q$, interpretable via a field-dependent diffeomorphism. The paper confirms predictions in a deformed free-fermion model and discusses potential Virasoro enhancements, UV properties, and holographic connections to warped CFT and Kerr/CFT. Overall, it extends the landscape of exactly solvable deformations of 2D QFTs, with implications for non-locality, UV completions, and holographic dualities.

Abstract

It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator $T \bar T$, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that posess a conserved $U(1)$ current, $J$. The deformation takes the schematic form $J \bar T$ and is interesting because it preserves an $SL(2,\mathbb{R}) \times U(1)$ subgroup of the original global conformal symmetries. For the case of a purely (anti)chiral current, we find the finite-size spectrum of the deformed theory and study its thermodynamic properties. We test our predictions in a simple example involving deformed free fermions.