A brute-force search for R-symmetric Wess-Zumino models

This work makes an exhaustive search for generic renormalizable R-symmetric Wess-Zumino models with up to 5 chiral fields, and checks the consistency of their vacuum solutions with predictions from the Nelson-Seiberg theorem and its generalizations. Each model is recorded as the R-charge assignment of fields, which uniquely determines the cubic polynomial superpotentials with generic coefficients. Redundancy from permutation symmetries and reducible models are properly eliminated in the searching algorithm. We found that among 859 models in total, 19 of them have supersymmetric vacua unpredicted by the Nelson-Seiberg theorem and its generalizations. These exceptional models have their specific R-charge assignments covered by constructions found in previous literature. The search result can be used to estimate the accuracy of the field counting method for finding supersymmetric models in the string landscape. More applications of the dataset are expected in future work.
Comment: 26 pages. v2: The search algorithm and results are updated and corrected. The full list of models and analysis of counterexamples are added in appendixes. v3: Counterexamples are rephrased as non-generic exceptions which do not contradict the Nelson-Seiberg. Discussion on computational complexity is added