The Nelson-Seiberg theorem revised

TL;DR

The paper revises the Nelson-Seiberg theorem for Wess-Zumino models, providing a necessary and sufficient condition for SUSY breaking that aids in model building and string phenomenology.

Contribution

It offers a revised, easily checkable version of the Nelson-Seiberg theorem that enhances SUSY model construction and analysis.

Findings

Revised the Nelson-Seiberg theorem to a necessary and sufficient condition.

Simplified criteria for identifying SUSY breaking vacua.

Enhanced tools for low energy SUSY model building and string phenomenology.

Abstract

The well-accepted Nelson-Seiberg theorem relates R-symmetries to supersymmetry (SUSY) breaking vacua, and provides a guideline for SUSY model building which is the most promising physics beyond the Standard Model. In the case of Wess-Zumino models with perturbative superpotentials, we revise the theorem to a combined necessary and sufficient condition for SUSY breaking which can be easily checked before solving the vacuum. The revised theorem provides a powerful tool to construct either SUSY breaking or SUSY vacua, and offers many practicable applications in low energy SUSY model building and string phenomenology.