Holomorphic Anomalies and the Nonrenormalization Theorem

It has been argued that the superpotential can be renormalized in the presence of massless particles. Possible implications which have been considered include the restoration of supersymmetry at higher loops or a shift to a supersymmetric vacuum state. We argue that even in the presence of massless particles, there are no new contributions to the superpotential at any order in perturbation theory. This confirms the utility of the Wilsonian superpotential for analyzing the moduli space of the low energy theory. Robert R. McCormick Fellow. Supported in part by DOE contract DF-FGP2-90ER40560. NSF Young Investigator Award, Alfred P. Sloan Foundation Fellowship, DOE Outstanding Junior Investigator Award. The supersymmetric nonrenormalization theorem [1] states that all perturbative corrections to the effective action come as contributions to the effective Kähler potential. In the presence of massless particles, however, it was noted in refs. [2]-[6], that certain infrared divergent contributions to the Kähler potential appear to be effectively superpotential renormalizations. An infrared divergent contribution to the Kähler potential of the following form can be rewritten as a superpotential interaction