Non-abelian bosonization from factored coset models in path integrals

TL;DR

This paper develops a path integral approach to derive abelian and non-abelian bosonization by decomposing the generating functional into a trivial coset model and a dynamic bosonic component, utilizing BRST symmetry.

Contribution

It introduces a novel derivation of bosonization using factored coset models within the path integral framework, highlighting the role of BRST symmetry.

Findings

Successful derivation of bosonization in path integral form

Identification of BRST symmetry facilitating smooth bosonization

Decomposition into trivial coset and dynamic bosonic parts

Abstract

We present a derivation of abelian and non-abelian bosonization in a path integral setting by expressing the generating functional for current-current correlation functions as a product of a $G/G$-coset model, which is dynamically trivial, and a bosonic part which contains the dynamics. A BRST symmetry can be identified which leads to smooth bosonization in both the abelian and non-abelian cases.