Abstract
We analyze theories in which a supersymmetric sector is coupled to a supersymmetry-breaking sector described by a non-linear realization. We show how to consistently couple N = 1 supersymmetric matter to non-supersymmetric matter in such a way that all interactions are invariant under non-linear supersymmetry transformations. We extend this formalism to couple N = 2 supersymmetric matter to N = 1 superfields that lack N = 2 partners but transform in a non-linear representation of the N = 2 algebra. In particular, we show how to couple an N = 2 vector to N = 1 chiral fields in a consistent way. This has important applications to effective field theories describing the interactions of D-brane world-volume fields with bulk fields. We apply our method to study systems where different sectors break different halves of supersymmetry, which appear naturally in models of intersecting branes.
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