Non Abelian Bosonization in Two and Three Dimensions

TL;DR

This paper develops a systematic path-integral approach to non-Abelian bosonization in two and three dimensions, deriving exact bosonization recipes and connecting fermionic determinants to Wess-Zumino-Witten and Chern-Simons actions.

Contribution

It introduces a systematic method to derive bosonization rules for fermions in 2D and 3D using fermion determinants and path integrals, linking to known topological actions.

Findings

Derivation of bosonization recipes for fermion currents

Connection of 2D fermions to Wess-Zumino-Witten action

Connection of 3D fermions to Chern-Simons action

Abstract

We discuss non-Abelian bosonization of two and three dimensional fermions using a path-integral framework in which the bosonic action follows from the evaluation of the fermion determinant for the Dirac operator in the presence of a vector field. This naturally leads to the Wess-Zumino-Witten action for massless two-dimensional fermions and to a Chern-Simons action for very massive three dimensional fermions. One advantage of our approach is that it allows to derive the exact bosonization recipe for fermion currents in a systematic way.