Super Yang-Mills in (11,3) dimensions

A supersymmetric Yang-Mills system in (11, 3) dimensions is constructed with the aid of two mutually orthogonal null vectors which naturally arise in a generalized spacetime superalgebra. An obstacle encountered in an attempt to extend this result to beyond 14 dimensions is described. A null reduction of the (11, 3) model is shown to yield the known super Yang-Mills model in (10, 2) dimensions. An (8, 8) supersymmetric super Yang-Mills system in (3, 3) dimensions is obtained by an ordinary dimensional reduction of the (11, 3) model, and it is suggested there may exist a superbrane with (3, 3) dimensional worldvolume propagating in (11, 3) dimensions.