Current Density Distributions and a Supersymmetric Action for Interacting Brane Systems

We propose a method to obtain a manifestly supersymmetric action functional for interacting brane systems. It is based on the induced map of the worldvolume of low-dimensional branes into the worldvolume of the space-time filling brane ((D-1)-brane), which may be either dynamical or auxiliary, and implies an identification of Grassmann coordinate fields of lower dimensional branes with an image of the Grassmann coordinate fields of that (D-1)-brane. With this identification the covariant current distribution forms with support on the superbrane worldvolumes become invariant under the target space supersymmetry and can be used to write the coupled superbrane action as an integral over the D-dimensional manifolds ((D-1)-brane worldvolume). We compare the equations derived from this new ('Goldstone fermion embedded') action with the ones produced by a more straightforward generalization of the free brane actions based on the incorporation of the boundary terms with Lagrange multipliers ('superspace embedded' action). We find that both procedures produce the same equations of motion and thus justify each other. Both actions are presented explicitly for the coupled system of a D=10 super-D3-brane and a fundamental superstring which ends on the super-D3-brane.