Dynamical gauge symmetry breaking and superconductivity in three-dimensional systems

We discuss dynamical breaking of non-Abelian gauge groups in three-dimensional (lattice) gauge systems via the formation of fermion condensates. A physically relevant example, motivated by condensed matter physics, is that of a fermionic gauge theory with group SU(2) x U-S(1) x U-E(1). In the strong U-S(1) region, the SU(2) symmetry breaks down to a U(1), due to the formation of a parity-invariant fermion condensate. We conjecture a phase diagram for the theory involving a critical line, which separates the regions of broken SU(2) symmetry from those where the symmetry is restored. In the broken phase, the effective Abelian gauge theory is closely related to an earlier model of two-dimensional parity-invariant superconductivity in doped antiferromagnets. The superconductivity in the model occurs in the Kosterlitz-Thouless mode, since strong phase fluctuations prevent the existence of a local order parameter. Some physical consequences of the SU(2) x U-S(1) phase diagram for the (doping-dependent) parameter space of this condensed matter model are briefly discussed.