Dynamical violation of parity and chiral symmetry in three-dimensional four-Fermi theory

Abstract

We study dynamical symmetry breaking in (2+1)-dimensional quantum electrodynamics with four-Fermi couplings. Using the large-$N$ expansion and an effective potential method we show that the four-Fermi couplings can be relevant when the coupling constants are near certain critical points. We show that the four-Fermi interactions can break either parity and time-reversal symmetries or a certain discrete flavor symmetry and analyze how the symmetry-breaking pattern is modified by electromagnetic interactions. We discuss the critical behavior of the theory in the large-$N$ expansion in both the leading and next-to-leading orders.