Abstract
We construct the space of super light rays for a D=10, N=1 superconformal structure. A super Ward correspondence is then established between D=10, N=1 supersymmetric Yang–Mills field equations on 10-dimensional spaces of the form M 4× M 6 (where M 4 is a four-dimensional complex space–time and M 6 is six-dimensional complex Minkowski space) and superbundles over the space of super light rays which are trivial on normal embedded quadrics. This result reduces in four dimensions to the equivalence of connections satisfying the D=4, N=4 SSYM field equations and superconnections integrable along super light rays also satisfying an added geometrical constraint coming from dimensional reduction. This extends the work of Witten and of Harnad and Shnider done on flat Minkowski space.
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