Higher-Derivative Terms in N=2 Supersymmetric Effective Actions

TL;DR

This paper develops a systematic method to construct higher-derivative terms in N=2 supersymmetric effective actions using harmonic superspace, revealing new holomorphic terms and non-renormalization properties.

Contribution

It introduces a novel approach to derive higher-derivative terms in N=2 supersymmetry, including a new 3-derivative mixed branch term and insights into superspace locality.

Findings

Identified holomorphic higher-derivative terms with non-renormalization properties.

Discovered a new 3-derivative mixed branch term as a superspace integral.

Showed Wess-Zumino terms only appear on mixed branches in N=2 SQCD.

Abstract

We show how to systematically construct higher-derivative terms in effective actions in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. Making an assumption about the absence of certain superspace Chern-Simons-like terms involving vector multiplets, we write all 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. These holomorphic terms include a novel 3-derivative term on mixed branches given as an integral over 3/4 of superspace. As an illustration of our method, we search for Wess-Zumino terms in the low energy effective action of N=2 supersymmetric QCD. We show that such terms occur only on mixed branches. We also present an argument showing that the combination of space-time locality with supersymmetry implies locality in the anticommuting superspace coordinates of for unconstrained superfields.