Nonexistence of supersymmetry breaking counterexamples to the Nelson-Seiberg theorem

TL;DR

This paper proves that certain types of counterexamples to the Nelson-Seiberg theorem, which predicts conditions for supersymmetry breaking, do not exist under specific R-symmetry conditions, refining the classification of these models.

Contribution

It establishes a nonexistence theorem showing that no counterexamples with supersymmetry breaking vacua occur when models lack R-symmetry or have specific R-charge configurations.

Findings

Counterexamples with supersymmetry breaking vacua do not exist under certain R-symmetry conditions.

Generic superpotentials always yield supersymmetric vacua without specific R-charge arrangements.

The result refines the classification of R-symmetric Wess-Zumino models.

Abstract

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.