Couplings in Pseudo-Supersymmetry

TL;DR

This work develops a consistent framework for couplings between sectors with linear and non-linear realizations of supersymmetry, motivated by D-brane and intersecting-brane setups where different sectors break different halves of SUSY. By promoting fields to composite hat-fields via replacements like $\\theta \\to - \\kappa \\lambda_g$ and constructing gauge-covariant non-linear transformations, the authors derive invariant actions for ${\\cal N}=1$ and ${\\cal N}=2$ multiplets coupled to non-supersymmetric matter. They extend the formalism to partially broken extended SUSY, including an ${\\cal N}=2$ goldstino sector and its coupling to ${\\cal N}=1$ matter, and analyze pseudo-supersymmetry in brane configurations, showing loop-order patterns for mass corrections and gravitino masses. The results provide a systematic EFT toolkit for describing bulk-boundary interactions in string-inspired models with non-local SUSY breaking and have potential relevance for D-brane world-volume dynamics and their couplings to bulk fields.

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.