New avenues in supersymmetry and supergravity

We analyze the problem of constructing supersymmetric versions of gauge theories of particles and of gravity which have a closed supersymmetric algebra. Inparticular we present the basic no-go theorems that indicate that in four dimensions it is not possible to construct suitably extended supersymmetric versions of the above theories without drastic modification of the supersymmetric algebra. Two ways past the“N=3” barrier are discussed; that of central charges involved highly constrained versions which appearn difficult to quantize effectively, while the use of light-cone variables seems to be the most promising. We give light-cone gauge versions of supersymmetric Yang-Mills theories for all extended cases of interest and briefly consider their ultraviolet divergence properties.