The Nelson-Seiberg theorem generalized with nonpolynomial superpotentials

TL;DR

This paper extends the Nelson-Seiberg theorem to include models with nonpolynomial superpotentials, establishing conditions for supersymmetry and R-symmetry breaking in a broader class of theories.

Contribution

It generalizes the Nelson-Seiberg theorem to nonpolynomial superpotentials, providing a unified criterion for supersymmetry breaking applicable to both perturbative and nonperturbative models.

Findings

Singularity at the origin indicates R-symmetry and supersymmetry breaking.

Generalized necessary and sufficient condition for supersymmetry breaking.

Applicable to a wider class of models beyond polynomial superpotentials.

Abstract

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.