Novel counterexample to the Nelson-Seiberg theorem

TL;DR

This paper introduces a new counterexample to the Nelson-Seiberg theorem using a specific R-symmetric Wess-Zumino model, challenging previous assumptions about R-symmetries and supersymmetry breaking.

Contribution

It presents a novel counterexample with unique R-charge assignments that bypasses earlier conditions, highlighting unresolved issues in the relation between R-symmetries and supersymmetry breaking.

Findings

Counterexample model with nine chiral superfields.

Model exhibits degenerate supersymmetric vacua with non-zero R-charges.

Escapes previous sufficient conditions for counterexamples.

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.