Couplings in pseudosupersymmetry

Abstract

We analyze theories in which a supersymmetric sector is coupled to a supersymmetry-breaking sector described by a nonlinear realization. We show how to consistently couple $\mathcal{N}=1$ supersymmetric matter to nonsupersymmetric matter in such a way that all interactions are invariant under nonlinear supersymmetry transformations. We extend this formalism to couple $\mathcal{N}=2$ supersymmetric matter to $\mathcal{N}=1$ superfields that lack $\mathcal{N}=2$ partners but transform in a nonlinear representation of the $\mathcal{N}=2$ algebra. In particular, we show how to couple an $\mathcal{N}=2$ vector to $\mathcal{N}=1$ 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.