The renormalization group and the effective potential in the Wess–Zumino model

Abstract

We consider the effective potential V in the massless Wess–Zumino model. By using the renormalization group equation, we show that the explicit and implicit dependence of V on the renormalization mass scale μ cancels. If V has an extremum at some non-vanishing value of the background field, then it follows that V is “flat”, independent of the background field. This is consistent with the general requirement that V be convex. The consequences for supersymmetric gauge theories are briefly considered.