Nonexistence of supersymmetry breaking counterexamples to the Nelson-Seiberg theorem

Abstract

Counterexample models to the Nelson-Seiberg theorem have been discovered, and their features have been studied in previous literature. All currently known counterexamples have generic superpotentials respecting the R-symmetry, and more R-charge 2 fields than R-charge 0 fields. But they give supersymmetric vacua with spontaneous R-symmetry breaking, thus violate both the Nelson-Seiberg theorem and its revisions. This work proves that the other type of counterexamples do not exist. When there is no R-symmetry, or there are no more R-charge 2 fields than R-charge 0 fields in models with R-symmetries, generic superpotentials always give supersymmetric vacua. There exists no specific arrangement of R-charges or non-R symmetry representations which makes a counterexample with a supersymmetry breaking vacuum. This nonexistence theorem contributes to a refined classification of R-symmetric Wess-Zumino models.

Gaugino Masses from Misaligned Supersymmetry Breaking and R-Symmetry Breaking Spurions

“…The R-charge assignment of fields determines the generic form of the superpotential, which has R-charge 2. SUSY or SUSY breaking vacua can be obtained by a proper R-charge assignment satisfying certain conditions [10][11][12][13][14][15][16][17][18][19][20]. SUSYbreaking effects are transferred to the visible sector through the coupling of messenger fields.…”

A formal notion of genericity and term-by-term vanishing superpotentials at supersymmetric vacua from R-symmetric Wess-Zumino models

“…The relation between R-symmetries and supersymmetry (SUSY) breaking [1] in generic Wess-Zumino models [2][3][4] is described by the Nelson-Seiberg theorem [5] and its several recent extensions [6][7][8][9], including counterexamples with generic parameters and special R-charge assignments [10][11][12][13]. This lore has manifested in the study of both SUSY phenomenology [14][15][16][17][18] and string phenomenology [19][20][21][22][23].…”