Two-loop effective potential for the Wess-Zumino model in 2+1 dimensions

By using superfield techniques, the effective potential of the $\mathcal{N}=1$ Wess-Zumino model in 2+1 dimensions is computed off-shell up to two loops. It is shown that supersymmetry is not dynamically broken, and that dynamical generation of mass does not occur perturbatively. We also investigate the renormalization of the effective potential and determine the renormalization group gamma and beta functions, showing that this model is infrared free. Comparison with some other results in the literature is provided.