Off-shell superspace D = 10 super-Yang-Mills from a covariantly quantized Green-Schwarz superstring

We construct a gauge-invariant superspace action in terms of unconstrained off-shell superfields for the D = 10 supersymmetric Yang-Mills (SYM) theory. We use to this effect: 1. (i) the point particle limit of the BRST charge of the covariantly quantized harmonic Green-Schwarz superstring, 2. (ii) a general covariant action principle for overdetermined systems of nonlinear field equations of motion. One obtains gauge and super-Poincaré invariant equations of motion equivalent to the Nilsson's constraints for D = 10 SYM. In the previous approaches (light-cone-gauge, component-fields) one would have to sacrifice either explicit Lorentz invariance or explicit supersymmetry while in the present approach they are both manifest. Unfortunately the action we find is nonlocal in space-time. To restore locality one may have to introduce additional degrees of freedom.