The Nelson-Seiberg theorem relates -symmetries to -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 -symmetric superpotential, a singularity at the origin of the field space implies both -symmetry breaking and supersymmetry breaking. We give a generalized necessary and sufficient condition for supersymmetry breaking which applies to both perturbative and nonperturbative models.

中文翻译：

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非多项式超势泛化的Nelson-Seiberg定理

纳尔逊- Seiberg及定理涉及-对称性来-长期超对称性破并提供超越标准模型的新物理模型建设的指导原则。定理的修正为具有多项式超势的模型中的超对称破坏提供了充要条件。这项工作重新审视了该定理，以包括具有非多项式超势的模型。随着通用-对称超势，在外地空间的原点的奇点隐含了-对称性破缺和超对称破。我们给出了超对称破坏的一般充要条件，该条件既适用于扰动模型也适用于非扰动模型。