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

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, within a quadratic approximation in the fields, to three different but equivalent bosonic theories: a nonlocal Maxwell--Chern-Simons--type theory, a nonlocal 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.