Couplings in pseudosupersymmetry

We analyze theories in which a supersymmetric sector is coupled to asupersymmetry-breaking sector described by a non-linear realization. We showhow to consistently couple N=1 supersymmetric matter to non-supersymmetricmatter in such a way that all interactions are invariant under non-linearsupersymmetry transformations. We extend this formalism to couple N=2supersymmetric matter to N=1 superfields that lack N=2 partners but transformin a non-linear representation of the N=2 algebra. In particular, we show howto couple an N=2 vector to N=1 chiral fields in a consistent way. This hasimportant applications to effective field theories describing the interactionsof D-brane world-volume fields with bulk fields. We apply our method to studysystems where different sectors break different halves of supersymmetry, whichappear naturally in models of intersecting branes.Comment: Latex, 30 pages, v2: references added and minor corrections, v3: normalization of fermions in N=2 vector corrected and references adde