SUPERBRANES

We consider the doubly supersymmetric formulation of various p-branes, that is, we replace the worldsurface of a super p-brane by a super wo rldsurface and consider the embedding of the latter into a target supe rspace. The number of worldsurface fermionic coordinates is taken to b e half as many as those of the target superspace. We show that a simpl e geometrical constraint and its integrability condition lead to manif estly worldsurface supersymmetric field equations for a large class of super p-branes. We illustrate this procedure in some detail in the ca se of the D = 11 superfivebrane. We also describe a class of super p-b ranes in which a worldsurface linear supermultiplet arises. In some ca ses we show that an additional constraint involving the curvature of a n appropriate worldsurface antisymmetric tensor potential is needed to put the theory on-shell.