  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.
