S-Dual of Maxwell Chern-Simons Theory

TL;DR

This paper explores the S-duality of three-dimensional Maxwell theory with a Chern-Simons term, proposing a dual description involving a non-gauge field and analyzing its implications and string theory connections.

Contribution

It introduces an S-dual formulation of Maxwell-Chern-Simons theory with a non-gauge field, expanding understanding of dualities in lower-dimensional gauge theories.

Findings

Proposes an S-dual description involving a non-gauge 1-form field.

Shows the dual theory includes a level k U(1) Chern-Simons term.

Discusses couplings to external currents and string theory realizations.

Abstract

We discuss the dynamics of three dimensional Maxwell theory coupled to a level $k$ Chern-Simons term. Motivated by S-duality in string theory we argue that the theory admits an S-dual description. The S-dual theory contains a non-gauge 1-form field, previously proposed by Deser and Jackiw and a level $k$ $U(1)$ Chern-Simons term, $Z_{\rm MCS}=Z_{\rm DJ}Z_{\rm CS}$. The couplings to external electric and magnetic currents and their string theory realisations are also discussed.