The Nelson-Seiberg theorem revised

We show that a cosmic string associated with spontaneous U(1) R symmetry breaking gives a constraint for supersymmetric model building. In some models, the string can be viewed as a tube-like domain wall with a winding number interpolating a false vacuum and a true vacuum. Such string causes inhomogeneous decay of the false vacuum to the true vacuum via rapid expansion of the radius of the tube and hence its formation would be inconsistent with the present Universe. However, we demonstrate that there exist metastable solutions which do not expand rapidly. Furthermore, when the true vacua are degenerate, the structure inside the tube becomes involved. As an example, we show a "bamboo"-like solution, which suggests a possibility observing an information of true vacua from outside of the tube through the shape and the tension of the tube.

mentioning

confidence: 63%

“…As shown in Eq. (3.11), reflecting the Z 2 symmetry of the model, there are two different R-tubes 5 . The one has γ = +1 and the other has γ = −1.…”

Section: Bamboo Solution: Tube Junctionmentioning

confidence: 99%

See 1 more Smart Citation

Cosmic R-string, R-tube and vacuum instability

Eto

Hamada

Kamada

et al. 2013

“…In 4-dimentinal N = 1 supersymmetry (SUSY) theories [1,2], the relation between SUSY breaking and R-symmetries in Wess-Zumino models are described by the Nelson-Seiberg theorem and its extensions [3][4][5][6]. The original Nelson-Seiberg theorem [3] states that for SUSY breaking at a stable vacuum in a generic model, a necessary condition is to have an R-symmetric superpotentical, and a sufficient condition is to have the R-symmtery spontaneously broken at the vacuum.…”

Section: Introductionmentioning

confidence: 99%

“…The statement can be extended to metastable SUSY breaking models with approximate R-symmetries [7][8][9]. A revised theorem [5] claims that with a polynomial superpotential, the neccessary and sufficient condition for SUSY breaking is to have an R-symmetric superpotentical and more R-charge 2 fields than R-charge 0 fields. The revised theorem can be generalized to include models with non-polynomial superpotentials [6], where the condition for SUSY breaking is the same as before for superpotentials smooth at the origin of the field space, and a singularity at the origin implies both R-symmetry breaking and supersymmetry breaking.…”

Section: Introductionmentioning

confidence: 99%

A counterexample to the Nelson-Seiberg theorem

Sun

Tan

Yang

2020

Self Cite

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.

A sufficient condition for counterexamples to the Nelson-Seiberg theorem

Sun

Tan

Yang

2021

Self Cite

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.