Non abelian bosonisation in three dimensional field theory

TL;DR

This paper develops a method for bosonisation in 2+1 dimensions, revealing a nonabelian gauge theory structure for the SU(2) massive Thirring model and connecting it to SU(2) Yang-Mills Chern-Simons theory in certain limits.

Contribution

It introduces a generalized St"uckelberg-based approach to bosonisation in three dimensions, explicitly deriving the physical sector and identities for fermionic currents.

Findings

Bosonised theory is a nonabelian gauge theory for arbitrary coupling.

In the zero coupling limit, it reduces to SU(2) Yang-Mills Chern-Simons theory.

Bosonisation identities for fermionic currents are established.

Abstract

We develop a method based on the generalised St\"uckelberg prescription for discussing bosonisation in the low energy regime of the SU(2) massive Thirring model in 2+1 dimensions. For arbitrary values of the coupling parameter the bosonised theory is found to be a nonabelian gauge theory whose physical sector is explicitly obtained. In the case of vanishing coupling this gauge theory can be identified with the SU(2) Yang-Mills Chern-Simons theory in the limit when the Yang-Mills term vanishes. Bosonisation identities for the fermionic current are derived.