Abstract (Elsevier)
In this paper we present the group manifold formulation of N =1, D =10 and N =4, D =4 super Yang-Mills theory. Our result is an off-shell, first-order action in superspace without central charges. Analysis of the Bianchi identities based on a general group theoretical technique described in a previous publication shows that no constraint can be imposed on the curvatures without implying propagation equations. This suggests that our first-order action is probably the only off-shell one: no second-order, off-shell formulation seems to exist.