Constrained superpotentials in harmonic gauge theories with 8 supercharges

TL;DR

This paper develops a harmonic superspace framework for D-dimensional supersymmetric gauge theories with 8 supercharges, deriving effective actions and superpotentials satisfying specific constraints and equations.

Contribution

It introduces a novel harmonic superspace approach to construct effective superfield actions with constrained superpotentials in theories with 8 supercharges.

Findings

Effective D=5 action includes free and Chern-Simons terms.

Superfield actions in D<4 are expressed via superpotentials obeying Laplace equations.

Discussion of alternative harmonic structures enhances theoretical understanding.

Abstract

We consider D-dimensional supersymmetric gauge theories with 8 supercharges (D<6,$~\mathcal{N}=8$) in the framework of harmonic superspaces. The effective Abelian low-energy action for D=5 contains the free and Chern-Simons terms. Effective $\mathcal{N}=8$ superfield actions for D<4 can be written in terms of the superpotentials satisfying the superfield constraints and (6-D)-dimensional Laplace equations. The role of alternative harmonic structures is discussed.