Field Dependent Gauge Couplings in Locally Supersymmetric Effective Quantum Field Theories

TL;DR

This paper explores how gauge couplings in locally supersymmetric quantum field theories depend on fields, emphasizing the role of Wess-Zumino terms, anomalies, and non-perturbative effects in maintaining supersymmetric consistency and their implications for string unification.

Contribution

It provides a detailed analysis of the field dependence of gauge couplings, highlighting the importance of Wess-Zumino terms and anomalies in both perturbative and non-perturbative regimes within supergravity.

Findings

Wess-Zumino terms affect gauge couplings at one-loop level.

Non-holomorphic field dependence of effective gauge couplings due to anomalies.

Specific superpotential form ensures consistency of scalar potential with supersymmetry.

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.