(p,q)-strings and New Spacetime Superalgebras

We present a geometric formulation of $(p,q)$-strings in which the $Sl(2;Z)$-doublet of the two-form gauge potentials is constructed as second order in the supersymmetric currents. The currents are constructed using a supergroup manifold corresponding to the $(p,q)$-string superalgebra, which contains fermionic generators in addition to the supercharges and transforms under the $Sl(2;Z)$. The properties of the superalgebra and the generalizations to higher $p$-branes are discussed.