S-Dual of Maxwell Chern-Simons Theory

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, $Z_{\mathrm{MCS}}=Z_{\mathrm{DJ}}{Z}_{\mathrm{CS}}$. The couplings to external electric and magnetic currents and their string theory realisations are also discussed.

11 pages,LaTex. 3 figures. v2: Few comments added, in particular how to incorporate dynamical matter. Version to appear in PRL

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