Harmonic-Superspace Integrability of N=1, D=6 Supersymmetric Gauge Theory

TL;DR

This paper explores the integrability of N=1, D=6 supersymmetric gauge theory using harmonic superspace, revealing a zero-curvature formulation and analyzing solutions for the SU(2) gauge group.

Contribution

It introduces a harmonic-superspace framework for understanding the integrability of N=1, D=6 supersymmetric gauge theories, including solution properties and gauge choices.

Findings

Zero-curvature formulation of the gauge equations

Analysis of SU(2) gauge group solutions in harmonic gauge

Discussion of integrability in supersymmetric gauge-matter systems

Abstract

We consider the harmonic-superspace ($HS$) system of equations that contains superfield $SYM^1_6$ constraints and equations of motion. A dynamical equation in the special $A$-frame is equivalent to the zero-curvature equation corresponding to a covariant conservation of $HS$-analyticity. Properties of a general $SYM^1_6$ solution for the gauge group $SU(2)$ are studied in the simplest harmonic gauge. An analogous approach to the integrability interpretation of $SYM$-$SG$-matter systems in $HS$ is discussed briefly.