Bosonization of Three Dimensional Non-Abelian Fermion Field Theories

TL;DR

This paper explores the bosonization of three-dimensional non-Abelian fermion theories, revealing their relation to Yang-Mills-Chern-Simons gauge theories and providing insights into low-energy behaviors.

Contribution

It demonstrates how the $SU(N)$ massive Thirring model bosonizes into gauge theories, specifically relating to $SU(N)$ Yang-Mills-Chern-Simons theories at low energies.

Findings

Bosonization relates the Thirring model to gauge theories.

For free massive fermions, bosonization yields pure Chern-Simons theory.

The relation is approximate, not exact.

Abstract

We discuss bosonization in three dimensions of an $SU(N)$ massive Thirring model in the low-energy regime. We find that the bosonized theory is related (but not equal) to $SU(N)$ Yang-Mills-Chern-Simons gauge theory. For free massive fermions bosonization leads, at low energies, to the pure $SU(N)$ (level $k=1$) Chern-Simons theory.