Field Dependent Gauge Couplings in Locally Supersymmetric Effective Quantum Field Theories

TL;DR

The paper develops a field-theoretic framework for gauge couplings in four-dimensional locally supersymmetric effective field theories with moduli. It shows that Weyl rescaling introduces a Wess-Zumino term that shifts Wilsonian gauge couplings at one loop, while physical, momentum-dependent couplings acquire non-holomorphic moduli dependence from Konishi and super-Weyl anomalies. It then derives a holomorphic effective superpotential that encodes non-perturbative dynamics, enabling exact relations for gaugino condensates, threshold effects, and the moduli potential. The work applies these results to hidden sectors and string unification, yielding insights into moduli stabilization, vacuum structure, and possible SUSY-breaking scenarios in realistic 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.