Self-duality and oblique confinement in planar gauge theories

We investigate the non-perturbative structure of two planar Z_p × Z_p lattice gauge models and discuss their relevance to two-dimensional condensed matter systems and Josephson junction arrays. Both models involve two compact U(1) gauge fields with Chern-Simons interactions, which break the symmetry down to Z_p × Z_p. By identifying the relevant topological excitations (instantons) and their interactions we determine the phase structure of the models. Our results match observed quantum phase transitions in Josephson junction arrays and suggest also the possibility of oblique confining ground states corresponding to quantum Hall regimes for either charges or vortices.