Super-Zeeman Embedding Models on N-Supersymmetric World-Lines

We construct a model of an electrically charged magnetic dipole with arbitrary N-extended world-line supersymmetry, which exhibits a supersymmetric Zeeman effect. By including supersymmetric constraint terms, the ambient space of the dipole may be tailored into an algebraic variety, and the supersymmetry broken for almost all parameter values. The so exhibited obstruction to supersymmetry breaking refines the standard one, based on the Witten index alone.