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

Abstract

It is known in previous literature that if a Wess-Zumino model with an R-symmetry gives a supersymmetric vacuum, the superpotential vanishes at the vacuum. In this work, we establish a formal notion of genericity, and show that if the R-symmetric superpotential has generic coefficients, the superpotential vanishes term-by-term at a supersymmetric vacuum. This result constrains the form of the superpotential which leads to a supersymmetric vacuum. It may contribute to a refined classification of Rsymmetric Wess-Zumino models, and find applications in string constructions of vacua with small superpotentials. A similar result for a scalar potential system with a scaling symmetry is discussed.

A novel counterexample to the Nelson-Seiberg theorem

“…Just like any SUSY vacuum in R-symmetric models, the SUSY vacua in the new counterexample give W = 0 at the SUSY vacuum [10,11,16], and the supergravity version of the model also gives SUSY vacua with zero vacuum energy. One may hope use the supergravity model as a low energy effective description for flux compactification of type IIB string theory [17,18,19,20], and such string constructions of W = 0 SUSY vacua [21,22,23,24,25,26,27] serve as the first step toward vacua with small superpotentials [28].…”

“…with a one complex dimensional degeneracy parameterized by the non-zero VEV of B. Like any SUSY vacuum in generic R-symmetric models, the vacua have the property that the superpotential vanishes term-by-term [10] and satisfies the bound found in [11]. The Rsymmetry is spontaneously broken everywhere on the degeneracy by all the non-zero VEVs of B, C and A i .…”

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

“…Since a SUSY vacuum satisfies ∂ i W = 0, the consistency between ( 101) and ( 102) means W = 0 at the vacuum. Moreover, it can be proved that an R-symmetric W vanishes termby term at a SUSY vacuum if its coefficients are generic [95]. Suppose the superpotential is constructed from a set of terms {p α (φ i )} allowed by a certain set of conditions including the R-symmetry:…”

Gaugino masses from misaligned supersymmetry breaking and R-symmetry breaking spurions

“…To build a natural SUSY breaking model in the hidden sector, it is necessary to introduce an R-symmetry which restricts the possible terms appearing in the superpotential [9]. The R-charge assignment of fields determines the generic form of the superpotential which has R-charge 2, and 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]. SUSY breaking effects are then transferred to the visible sector through the coupling of messenger fields.…”