GAUGE-THEORIES OF JOSEPHSON-JUNCTION ARRAYS

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chem-Simons term describing the charge-v ortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase tra nsition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantu m Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge -vortex coupling can lead to transitions to anyon superconductivity ph ases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetri c Kalb-Ramond gauge field.