SPONTANEOUS CHIRAL-SYMMETRY BREAKING IN 3-DIMENSIONAL QED WITH A CHERN-SIMONS TERM

In three-dimensional QED with a Chern-Simons term we study the phase structure associated with chiral-symmetry breaking in the framework of the Schwinger-Dyson equation. We give detailed analyses on the analytical and numerical solutions for the Schwinger-Dyson equation of the fermion propagator, where the nonlocal gauge-fixing procedure is adopted to avoid wave-function renormalization for the fermion. In the absence of the Chern-Simons term, there exists a finite critical number of four-component fermion flavors, at which a continuous (infinite-order) chiral phase transition takes place and below which the chiral symmetry is spontaneously broken. In the presence of the Chern-Simons term, we find that the spontaneous chiral-symmetry-breaking transition continues to exist, but the type of phase transition turns into a discontinuous first-order transition. A simple stability argument is given based on the effective potential, whose stationary point gives the solution of the Schwinger-Dyson equation.