An integrable Lorentz-breaking deformation of two-dimensional CFTs

TL;DR

This paper explores a universal Lorentz-breaking deformation of 2D CFTs with a conserved U(1) current, analyzing its spectrum and thermodynamics, and providing explicit results for free fermions.

Contribution

It introduces and solves a new $J ar T$ deformation of 2D CFTs that preserves certain symmetries and extends the solvability known from $T ar T$ deformations.

Findings

Finite-size spectrum derived for the deformed theories.

Thermodynamic properties analyzed and predicted.

Validation through a free fermion example.

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.