Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

TL;DR

This paper introduces an all-loop anisotropic bosonized Thirring sigma model that interpolates between well-known models, revealing a simple RG flow structure and connections to integrable systems.

Contribution

It develops a comprehensive all-loop RG flow analysis for the anisotropic Thirring model, including novel invariance properties and links to integrable systems.

Findings

RG flow equations have a simple form

Symmetric couplings recover previous results

Interpolates between Lagrange and Darboux-Halphen systems

Abstract

We study what we call the all-loop anisotropic bosonized Thirring sigma model. This interpolates between the WZW model and the non-Abelian T-dual of the principal chiral model for a simple group. It has an invariance involving the inversion of the matrix parametrizing the coupling constants. We compute the general renormalization group flow equations which assume a remarkably simple form and derive its properties. For symmetric couplings, they consistently truncate to previous results in the literature. One of the examples we provide gives rise to a first order system of differential equations interpolating between the Lagrange and the Darboux-Halphen integrable systems.