S-Dual of Maxwell Chern-Simons Theory

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, $Z_{\mathrm{M}\mathrm{C}\mathrm{S}}=Z_{\mathrm{D}\mathrm{J}}{Z}_{\mathrm{C}\mathrm{S}}$. The couplings to external electric and magnetic currents and their string theory realisations are also discussed.