On the Renormalization of Theories of a Scalar Chiral Superfield

An exact renormalization group for theories of a scalar chiral superfield is formulated, directly in four dimensional Euclidean space. By constructing a projector which isolates the superpotential from the full Wilsonian effective action, it is shown that the nonperturbative nonrenormalization theorem follows, quite simply, from the flow equation. Next, it is argued that there do not exist any physically acceptable non-trivial fixed points. Finally, the Wess-Zumino model is considered, as a low energy effective theory. Following an evaluation of the one and two loop beta-function coefficients, to illustrate the ease of use of the formalism, it is shown that the beta-function in the massless case does not receive any nonperturbative power corrections.