The Nelson-Seiberg Theorem Generalized with Nonpolynomial Superpotentials

The Nelson-Seiberg theorem relates -symmetries to -term supersymmetry breaking and provides a guiding rule for new physics model building beyond the Standard Model. A revision of the theorem gives a necessary and sufficient condition to supersymmetry breaking in models with polynomial superpotentials. This work revisits the theorem to include models with nonpolynomial superpotentials. With a generic -symmetric superpotential, a singularity at the origin of the field space implies both -symmetry breaking and supersymmetry breaking. We give a generalized necessary and sufficient condition for supersymmetry breaking which applies to both perturbative and nonperturbative models.