Gauge structure, anomalies, and mass generation in a three-dimensional Thirring model

We consider a three-dimensional model of spinor fields with a Thirring-like, quadrilinear self-interaction. Using either two- or four-component Dirac spinors, we prove that the 1/N expansion for the model is renormalizable if a gauge structure to select physical quantities is introduced. For certain values of the coupling, the leading 1/N approximation exhibits bound-state poles. Dynamical breaking of parity or chiral symmetry is shown to occur as a cooperative effect of different orders of 1/N, if N is smaller than the critical value Nc=128π²D, where D is two or four depending on whether the fermion field has two or four components.