A counterexample to the Nelson-Seiberg theorem

• Main Authors: Zheng Sun, Zipeng Tan, Lu Yang
• Format: Article
• Language: English
• Published: SpringerOpen 2020-10-01
• Series: Journal of High Energy Physics
• Subjects: Global Symmetries; Supersymmetry Breaking; Supersymmetric Effective Theories
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2020)072

Abstract We present a counterexample to the Nelson-Seiberg theorem and its extensions. The model has 4 chiral fields, including one R-charge 2 field and no R-charge 0 filed. Giving generic values of coefficients in the renormalizable superpotential, there is a supersymmetric vacuum with one complex dimensional degeneracy. The superpotential equals zero and the R-symmetry is broken everywhere on the degenerated vacuum. The existence of such a vacuum disagrees with both the original Nelson-Seiberg theorem and its extensions, and can be viewed as the consequence of a non-generic R-charge assignment. Such counterexamples may introduce error to the field counting method for surveying the string landscape, and are worth further investigations.