A counterexample to the Nelson-Seiberg theorem
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