Dual description of U(1) charged fields in (2+1) dimensions

TL;DR

This paper generalizes the functional bosonization method in (2+1) dimensions, establishing a duality between charged field theories and Abelian gauge theories, and explores the implications of Chern-Simons terms on spin and statistics.

Contribution

It introduces a generalized duality mapping for any conserved Abelian charge in (2+1) dimensions, with detailed analysis and explicit examples.

Findings

Dual Abelian gauge theories correspond to charged field theories in (2+1)D.

The Chern-Simons coefficient influences spin and statistics properties.

Explicit examples illustrate the duality and its physical implications.

Abstract

We show that the functional bosonization procedure can be generalized in such a way that, to any field theory with a conserved Abelian charge in (2+1) dimensions, there corresponds a dual Abelian gauge field theory. The properties of this mapping and of the dual theory are discussed in detail, presenting different explicit examples. In particular, the meaning and effect of the coefficient of the Chern-Simons term in the dual action is interpreted in terms of the spin and statistics connection.