The Nelson-Seiberg theorem generalized with nonpolynomial superpotentials (Q2208798)

Summary: The Nelson-Seiberg theorem relates \(R\)-symmetries to \(F\)-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 \(R\)-symmetric superpotential, a singularity at the origin of the field space implies both \(R\)-symmetry breaking and supersymmetry breaking. We give a generalized necessary and sufficient condition for supersymmetry breaking which applies to both perturbative and nonperturbative models.