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 s tructure associated with chiral-symmetry breaking in the framework of the Schwinger-Dyson equation. We give detailed analyses on the analyti cal and numerical solutions for the Schwinger-Dyson equation of the fe rmion propagator, where the nonlocal gauge-fixing procedure is adopted to avoid wave-function renormalization for the fermion. In the absenc e of the Chern-Simons term, there exists a finite critical number of f our-component fermion flavors, at which a continuous (infinite-order) chiral phase transition takes place and below which the chiral symmetr y is spontaneously broken. In the presence of the Chern-Simons term, w e find that the spontaneous chiral-symmetry-breaking transition contin ues to exist, but the type of phase transition turns into a discontinu ous 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.