Zero-curvature representation for harmonic-superspace equations of motion in $N=1, D=6$ supersymmetric gauge theory

TL;DR

This paper develops a zero-curvature representation for the equations of motion in six-dimensional N=1 supersymmetric gauge theory within harmonic superspace, providing a new framework for solving and analyzing these equations.

Contribution

It introduces a special harmonic gauge and a zero-curvature formulation that simplifies solving the supersymmetric gauge equations in six dimensions.

Findings

Derived superfield equations for the general $SYM^1_6$ solution

Established a zero-curvature representation for the equations of motion

Discussed potential applications to integrability conditions in related theories

Abstract

We consider the $SYM^1_6$ harmonic-superspace system of equations that contains superfield constraints and equations of motion for the simplest six-dimensional supersymmetric gauge theory. A special $A$-frame of the analytic basis is introduced where a kinematic equation for the harmonic connection $A^{\s--}$ can be solved . A dynamical equation in this frame is equivalent to the zero-curvature equation corresponding to the covariant conservation of analyticity. Using a simple harmonic gauge condition for the gauge group $SU(2)$ we derive the superfield equations that produce the general $SYM^1_6$ solution . An analogous approach for the analysis of integrability conditions for the $SYM^2_4$-theory and $SYM$-supergravity-matter systems in harmonic superspace is discussed briefly.