Higher-Derivative Terms in N=2 Supersymmetric Effective Actions

TL;DR

This work develops a systematic framework for constructing higher-derivative terms in $N=2$ supersymmetric effective actions using harmonic superspace, addressing redundancy from infinite auxiliary fields by reducing to a finite on-shell set at each derivative order. It classifies all possible 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches, highlighting holomorphic structures with non-renormalization properties and revealing that Wess-Zumino terms can arise only on mixed branches. The analysis relies on the harmonic-superspace formalism, constraints like analyticity and Bianchi identities, and a locality argument for Grassmann coordinates. It also discusses potential superspace Chern-Simons-like terms and shows that, under reasonable locality assumptions, such terms do not contribute at the orders studied. The results illuminate the structure of low-energy effective actions in $N=2$ theories and provide a concrete toolkit for deriving non-perturbative corrections and WZ couplings.

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.