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 α≡N $e^2$ of the gauge coupling constant, but the scale at which the self-mass begins to damp rapidly appears to be of order α, so that there is no spontaneous breaking of an approximate scale invariance that the underlying theory possesses at momentum small compared to α. 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.