A novel counterexample to the Nelson-Seiberg theorem

Abstract

We present a new type of counterexample to the Nelson-Seiberg theorem. It is a generic R-symmetric Wess-Zumino model with nine chiral superfields, including one field of R-charge 2 and no R-charge 0 field. As in previous counterexamples, the model gives a set of degenerate supersymmetric vacua with a non-zero expectation value for a pair of oppositely R-charged fields. However, one of these fields appears quadratically in the superpotential, and many other fields with non-zero R-charges gain non-zero expectation values at the vacuum, and so this model escapes the sufficient condition for counterexamples established in previous literature. Thus there are still open problems in the relation of R-symmetries to supersymmetry breaking in generic models.

Supersymmetry and R-symmetries in Wess-Zumino models: properties and model dataset construction

“…Their R-charge assignments satisfy the condition in Theorem 4. The dataset for N ≤ 5 contains no counterexample beyond Theorem 4 like the one in [57].…”

“…There is no special R-charge assignment which can give SUSY breaking counterexample with generic coefficients [56]. But new counterexamples with R-symmetry breaking SUSY vacua not covered by the sufficient condition are also found [57].…”

“…Another type of non-genericity comes from the combined requirements of R-symmetries and renormalization [53,54,55,56,57]. A renormalizable W has terms up to cubic.…”

“…But compared to N 2 and N 0 which are simple counts of fields with R-charge 2 and 0, identifying P 's and Q's according to (97) requires more elaboration of their appearance in superpotential terms. Furthermore, counterexamples not covered by Theorem 4 exist [57]. Therefore we stick to N 2 and N 0 to keep the field-counting method simple and efficient.…”

“…These non-generic counterexamples may introduce non-neglectable error to the field-counting method. Some counterexamples can be described as special arrangement of R-charges satisfying a sufficient condition [54,55,56], but new counterexamples not covered by the sufficient condition are also found [57]. Here we present a preliminary construction of the dataset of R-symmetric Wess-Zumino models [58].…”