Conformal Points and Duality of Non-Abelian Thirring Models and Interacting WZNW Models

TL;DR

This paper demonstrates a duality between the strong coupling phase of the non-Abelian Thirring model and the weak-coupling phase of coupled WZNW models, revealing integrability and critical behavior in these quantum field theories.

Contribution

It establishes a duality between non-Abelian Thirring models and coupled WZNW models, identifying critical points and their relation to conformal field theories and the Gross-Neveu model.

Findings

The strong coupling phase of the non-Abelian Thirring model is dual to the weak-coupling phase of coupled WZNW models.

At the critical point, the model reduces to a free fermion plus topological field theory.

The system is related to a perturbed conformal field theory with a nontrivial beta-function zero.

Abstract

We show that the strong coupling phase of the non-Abelian Thirring model is dual to the weak-coupling phase of a system of two WZNW models coupled to each other through a current-current interaction. This latter system is integrable and is related to a perturbed conformal field theory which, in the large $|k|$ limit, has a nontrivial zero of the perturbation-parameter beta-function. The non-Abelian Thirring model reduces to a free fermion theory plus a topological field theory at this critical point, which should therefore be identified with the isoscalar Dashen-Frishman conformal point. The relationship with the Gross-Neveu model is discussed.