Constraints and field equations for ten dimensional super Yang-Mills theory (Q1081140)

We give a complete proof of the equivalence between constraint equations and field equations for the \(d=10\), \(N=1\) supersymmetric Yang-Mills theory, a result proposed and partially proved recently by \textit{E. Witten} [Twistor-like transform in ten dimensions, Nucl. Phys., B 266, 245-264 (1986)]. Our approach explicitly reconstructs the superconnection satisfying the constraints from the on shell component fields. A key ingredient of the method is the choice of a suitable family of gauges, effectively eliminating all gauge dependence on anti-commuting coordinates. As a corollary, obtained by dimensional reduction, we also deduce the equivalence of constraints and field equations for the \(d=4\), \(N=4\) theory, as well as for \(d=6\), \(N=2\).