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

TL;DR

This paper formalizes the concept of genericity in R-symmetric Wess-Zumino models, proving that generic superpotentials vanish term-by-term at supersymmetric vacua, which aids in classifying such models and has implications for string theory vacua.

Contribution

It introduces a formal notion of genericity and demonstrates that generic R-symmetric superpotentials vanish term-by-term at supersymmetric vacua, refining model classification.

Findings

Superpotentials with generic coefficients vanish term-by-term at vacua.

The results constrain the form of superpotentials leading to supersymmetric vacua.

Potential applications in string theory constructions of vacua with small superpotentials.

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 R-symmetric 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.