The all-loop non-Abelian Thirring model and its RG flow

Abstract

We analyze the renormalization group flow in a recently constructed class of integrable σ-models which interpolate between WZW current algebra models and the non-Abelian T-duals of PCM for a simple group G. They are characterized by the integer level k of the current algebra, a deformation parameter λ and they exhibit a remarkable invariance involving the inversion of λ. We compute the β-function for λ to leading order in 1k. Based on agreement with previous results for the exact β-function of the non-Abelian bosonized Thirring model and matching global symmetries, we state that our integrable models are the resummed version (capturing all counterterms in perturbation theory) of the non-Abelian bosonized Thirring model for a simple group G. Finally, we present an analogous treatment in a simple example of a closely related class of models interpolating between gauged WZW coset CFTs and the non-Abelian T-duals of PCM for the coset G/H.