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

B. M. Zupnik
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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.

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B. M. Zupnik. 1995-12-06. Zero-curvature representation for harmonic-superspace equations of motion in $N=1, D=6$ supersymmetric gauge theory. https://arxiv.org/abs/hep-th/9512035

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