Harmonic-superspace integrability of N = 1, D = 6 supersymmetric gauge theory

We consider the harmonic-superspace (HS) system of equations that contains superfield SYM61 constraints and equations of motion. A dynamical equation in the special superfield variables is equivalent to the zero-curvature equation corresponding to a covariant conservation of HS-analyticity. Properties of a general SYM61 solution for the gauge group SU(2) are studied in the simplest harmonic gauge. An analogous approach to the integrability interpretation of SYM-supergravity-matter systems in HS is discussed briefly.