A sufficient condition for counterexamples to the Nelson-Seiberg theorem

Abstract

Several counterexample models to the Nelson-Seiberg theorem have been discovered in previous literature, with generic superpotentials respecting the R-symmetry and non-generic R-charge assignments for chiral fields. This work present a sufficient condition for such counterexample models: the number of R-charge 2 fields, which is greater than the number of R-charge 0 fields, must be less than or equal to the number of R-charge 0 fields plus the number of independent field pairs with opposite R-charges and satisfying some extra requirements. We give a correct count of such field pairs when there are multiple field pairs with degenerated R-charges. These models give supersymmetric vacua with spontaneous R-symmetry breaking, thus are counterexamples to both the Nelson-Seiberg theorem and its extensions.

Nonexistence of supersymmetry breaking counterexamples to the Nelson-Seiberg theorem

“…The technique in the proof of this work is also applicable in the proof of Theorem 4. The field classification in Theorem 4 leads to the generic superpotential [22] These equations form a balanced or under-determined system with effectively N Y + N P Q independent variables and N X ≤ N Y + N P Q quadratic polynomial equations. There are…”

“…While these relations have found successful applications in SUSY phenomenology beyond SM and compactification of string theory, counterexamples to the Nelson-Seiberg theorem and its revisions are constructed in literature, with generic superpotential coefficients and non-generic R-charges [20,21]. Their features are summarized into the following sufficient condition [22]:…”

“…These counterexamples have generic coefficients respecting symmetries and do not suffer from fine-tuning, thus are not neglectable in phenomenology studies. Their features are summarized into a sufficient condition [22], which produces a class of models covering all known counterexamples in the previous literature.…”

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].…”

“…The prediction is thus robust to small changes of parameters from a particular point in the parameter space, and no fine-tuning is needed. Although non-generic R-charges are mentioned in counterexamples to the Nelson-Seiberg theorem, they are more properly described as special R-charge assignments satisfying certain conditions [12]. We therefore focus on generic parameters in this work.…”