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

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 Witten [1]. 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 co-ordinates. 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.