Duality Equivalence Between Self-Dual And Topologically Massive Non-Abelian Models

TL;DR

This paper introduces a new gauge lifting technique to establish duality and equivalence between non-abelian self-dual models and Yang-Mills-Chern-Simons theory, overcoming limitations of previous methods.

Contribution

It presents a novel dualization method that is effective for non-abelian models and extends to cases with dynamical fermionic matter, surpassing the master action approach.

Findings

Established duality between non-abelian self-dual and Yang-Mills-Chern-Simons models

Generalized dual equivalence to include fermionic matter fields

Provided insights into 3D non-abelian bosonization

Abstract

The non-abelian version of the self-dual model proposed by Townsend, Pilch and van Nieuwenhuizen presents some well known difficulties not found in the abelian case, such as well defined duality operation leading to self-duality and dual equivalence with the Yang-Mills-Chern-Simons theory, for the full range of the coupling constant. These questions are tackled in this work using a distinct gauge lifting technique that is alternative to the master action approach first proposed by Deser and Jackiw. The master action, which has proved useful in exhibiting the dual equivalence between theories in diverse dimensions, runs into trouble when dealing with the non-abelian case apart from the weak coupling regime. This new dualization technique on the other hand, is insensitive of the non-abelian character of the theory and generalize straightforwardly from the abelian case. It also leads, in a simple manner, to the dual equivalence for the case of couplings with dynamical fermionic matter fields. As an application, we discuss the consequences of this dual equivalence in the context of 3D non-abelian bosonization.