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 currents, and hence is manifestly supersymmetric. The currents are constructed using a supergroup manifold corresponding to a generalization of a superalgebra which we found sometime ago. Our results generalize Siegel's analogous reformulation of the Green–Schwarz superstring. The new superalgebras we construct underly the free differential superalgebras introduced by de Azcárraga and Townsend a few years ago.