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

TL;DR

This paper conducts an exhaustive search for R-symmetric Wess-Zumino models with up to five chiral fields, identifying models with unexpected supersymmetric vacua and providing a dataset for further theoretical and string landscape studies.

Contribution

It provides the first comprehensive classification of R-symmetric Wess-Zumino models with up to five fields, including the discovery of models with supersymmetric vacua not predicted by existing theorems.

Findings

19 models with unexpected supersymmetric vacua

A dataset of 859 models with R-charge assignments

Validation of the field counting method in string landscape

Abstract

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.