Dualities and bosonization of massless fermions in three dimensional space-time

TL;DR

This paper explores the duality relations between massless fermions and various bosonic theories in three-dimensional space-time, establishing multiple equivalent bosonic descriptions through path-integral and operator methods.

Contribution

It introduces new duality relations showing that a massless fermion theory is equivalent to three different quadratic bosonic theories, including non-local and local models.

Findings

Fermionic theory is dual to a non-local Maxwell-Chern-Simons-type bosonic theory.

Fermionic theory is dual to a non-local self-dual-type vector bosonic theory.

Fermionic theory is dual to a local free massless bosonic theory.

Abstract

We study the bosonization of massless fermions in three-dimensional space-time. Using the path-integral approach as well as the operator formalism, we investigate new duality relations between fermionic and bosonic theories. In particular, we show that a theory of massless fermions is dual to three different, but equivalent bosonic theories which are quadratic in the bosonic fields: a non-local Maxwell- Chern-Simons-type theory, a non-local self-dual-type vector theory, and a local free massless bosonic theory. The equivalence is proven at the level of current correlation functions and current algebra analysis.