Nonexistence of supersymmetry breaking counterexamples to the Nelson-Seiberg theorem

Counterexample models to the Nelson-Seiberg theorem have been discovered, and their features have been studied in previous literature. All currently known counterexamples have generic superpotentials respecting the R-symmetry, and more R-charge 2 fields than R-charge 0 fields. But they give supersymmetric vacua with spontaneous R-symmetry breaking, thus violate both the Nelson-Seiberg theorem and its revisions. This work proves that the other type of counterexamples do not exist. When there is no R-symmetry, or there are no more R-charge 2 fields than R-charge 0 fields in models with R-symmetries, generic superpotentials always give supersymmetric vacua. There exists no specific arrangement of R-charges or non-R symmetry representations which makes a counterexample with a supersymmetry breaking vacuum. This nonexistence theorem contributes to a refined classification of R-symmetric Wess-Zumino models.

Global Nonexistence of Positive Initial-Energy Solutions for Coupled Nonlinear Wave Equations with Damping and Source Terms

This work is concerned with a system of nonlinear wave equations with nonlinear damping and source terms acting on both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy.

ANTI-COMMUTING REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS

In this paper we give a nonexistence theorem for real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) with anti-commuting shape operator.