  Using the superfield formalism, we study the dynamical breaking of gauge
symmetry in the N=1 three-dimensional supersymmetric Chern-Simons model,
coupled to a complex scalar superfield with a quartic self-coupling. This is an
analogue of the conformally invariant Coleman-Weinberg model in four spacetime
dimensions. We show that a mass for the gauge and matter superfields are
dynamically generated after two-loop corrections to the effective
superpotential. We also discuss the N=2 extension of our work, showing that the
Coleman-Weinberg mechanism in such model is not feasible, because it is
incompatible with perturbation theory.
