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.
Highlights
Where W = W is a function named the superpotential for a set of scalar fields {φi}
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
In this work, using the formal notion of genericity established in section 3, we proved that the expectation value of a generic R-symmetric superpotential vanishes term-by-term at a SUSY vacuum
Summary
In a Wess-Zumino model, a SUSY vacuum corresponds to a solution to the equations. where W = W (φi) is a function named the superpotential for a set of scalar fields {φi}. At a SUSY vacuum, field expectation values satisfy ∂iW = 0. The result of a vanishing W is general for any R-symmetric W which gives a SUSY vacuum, and does not depend on whether W is generic or not. With the R-charge assignment r(X1) = r(X2) = 2, r(Y ) = 0 It gives two infinite set of SUSY vacua at (2.10). Generic nonzero values of a, b, X1 and X2 make all terms of W nonzero, but these terms add up to zero, and W = 0 is satisfied at a SUSY vacuum. We are to show that such cancellation between terms does not happen in generic models: every term of W must vanish at a SUSY vacuum from a generic R-symmetric W
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