Integrable Lorentz-breaking deformations and RG flows

TL;DR

This paper constructs an all-loop effective action for Lorentz-breaking WZW model deformations, proves integrability for isotropic couplings, and identifies a non-perturbative symmetry with exact beta-functions that vanish in certain parameter regions.

Contribution

It provides a comprehensive all-loop effective action for Lorentz-breaking current deformations and reveals integrability and symmetries in specific coupling regimes.

Findings

Proved integrability for isotropic couplings.

Identified a non-perturbative symmetry of the effective action.

Computed exact beta-functions that vanish outside a bounded parameter region.

Abstract

We construct the all loop effective action for WZW models perturbed by current-bilinear terms of the type $J_+J_- $, $J_+J_+ $ and $J_-J_- $, the last two of which explicitly break Lorentz invariance. For isotropic couplings we prove integrability. For the case in which only the first two terms are present we identify a non-perturbative symmetry of the effective action and we compute the exact beta-functions. These become identically zero outside a bounded region in the parametric space.