Spontaneous chiral-symmetry breaking in three-dimensional QED

A detailed analysis is given of chiral-symmetry breaking in the large-flavor (N) limit of quantum electrodynamics in (2+1) dimensions. Analytical and numerical solutions of the homogeneous Dyson-Schwinger equation for the fermion self-energy combined with a computation of the effective potential for the fermion bilinear show that it is energetically preferable for the theory to dynamically generate a mass for fermions. The magnitude of the mass is roughly exponentially suppressed in N from the fundamental dimensionful scale N e2 of the gauge coupling constant, but the scale at which the self-mass begins to damp rapidly appears to be of order , so that there is no spontaneous breaking of an approximate scale invariance that the underlying theory possesses at momentum small compared to . Higher-order 1/N corrections are analyzed and it is shown that the 1/N expansion can be used consistently to demonstrate chiral-symmetry breaking. Open issues and possible improvements of the analysis are given and some avenues for future investigation suggested.