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

Abstract

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 $\frac{1}{N}$ expansion for the model is renormalizable if a gauge structure to select physical quantities is introduced. For certain values of the coupling, the leading $\frac{1}{N}$ approximation exhibits bound-state poles. Dynamical breaking of parity or chiral symmetry is shown to occur as a cooperative effect of different orders of $\frac{1}{N}$, if $N$ is smaller than the critical value ${N}_{c}=\frac{128}{{\ensuremath{\pi}}^{2}D}$, where $D$ is two or four depending on whether the fermion field has two or four components.