SUPER P-BRANE THEORIES AND NEW SPACETIME SUPERALGEBRAS

We present a geometric formulation of super p-brane theories in which the Wess-Zumino term is (p + 1)-th order in the supersymmetric current s, and hence is manifestly supersymmetric. The currents are constructe d using a supergroup manifold corresponding to a generalization of a s uperalgebra which we found sometime ago. Our results generalize Siegel 's analogous reformulation of the Green-Schwarz superstring. The new s uperalgebras we construct underly the free differential superalgebras introduced by de Azcarraga and Townsend a few years ago.