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 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.