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We construct a model of an electrically charged magnetic dipole witharbitrary N-extended world-line supersymmetry, which exhibits a supersymmetricZeeman effect. By including supersymmetric constraint terms, the ambient spaceof the dipole may be tailored into an algebraic variety, and the supersymmetrybroken for almost all parameter values. The so exhibited obstruction tosupersymmetry breaking refines the standard one, based on the Witten indexalone.

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