English

A counterexample to the Nelson-Seiberg theorem

High Energy Physics - Theory 2021-07-29 v4 High Energy Physics - Phenomenology

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.

Keywords

Cite

@article{arxiv.1904.09589,
  title  = {A counterexample to the Nelson-Seiberg theorem},
  author = {Zheng Sun and Zipeng Tan and Lu Yang},
  journal= {arXiv preprint arXiv:1904.09589},
  year   = {2021}
}

Comments

7 pages; v2: discussion on non-generic R-charges added, new references updated; v3: minor changes to notation and convention in formulas, JHEP pre-publication version

R2 v1 2026-06-23T08:45:40.064Z