Field Dependent Gauge Couplings in Locally Supersymmetric Effective Quantum Field Theories

Abstract

We investigate the field dependence of the gauge couplings of locally supersymmetric effective quantum field theories. We find that the Weyl rescaling of supergravity gives rise to Wess-Zumino terms that affect the gauge couplings at the one-loop level. These Wess-Zumino terms are crucial in assuring supersymmetric consistency of both perturbative and non-perturbative gauge interactions. At the perturbative level, we distinguish between the holomorphic Wilsonian gauge couplings and the physically-measurable momentum-dependent effective gauge couplings; the latter are affected by the Konishi and the super-Weyl anomalies and their field-dependence is non-holomorphic. At the non-perturbative level, we show how consistency of the scalar potential generated by infrared-strong gauge interactions with the local supersymmetry requires a very specific form of the effective superpotential. We use this superpotential to determine the dependence of the supersymmetric condensates of a strongly interacting gauge theory on its (field-dependent) Wilsonian gauge coupling and the Yukawa couplings of the matter fields. The article concludes with the discussion of the field-dependent non-perturbative phenomena in the context of string unification.