Revisiting arithmetic solutions to theW=0condition

Abstract

The gravitino mass is expected not to be much smaller than the Planck scale for a large fraction of vacua in flux compactifications. There is no continuous parameter to tune even by hand, and it seems that the gravitino mass can be small only as a result of accidental cancellation among period integrals weighted by integer-valued flux quanta. DeWolfe et.al. (2005) proposed to pay close attention to vacua where the Hodge decomposition is possible within a number field, so that the precise cancellation takes place as a result of algebra. We focus on a subclass of those vacua-those with complex multiplications-and explore more on the idea in this article. It turns out, in Type IIB compactifications, that those vacua admit non-trivial supersymmetric flux configurations if and only if the reflex field of the Weil intermediate Jacobian is isomorphic to the quadratic imaginary field generated by the axidilaton vacuum expectation value. We also found that flux statistics is highly enriched on such vacua, as F-term conditions become linearly dependent.

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

“…This result constrains the form of an R-symmetric Wess-Zumino model which leads to a SUSY vacuum: each term of the superpotential must contain at least one field with a zero expectation value. Such a constraint may lead to new extensions of the Nelson-Seiberg theorem, contribute to a refined classification of R-symmetric Wess-Zumino models, and find applications in string constructions of W = 0 SUSY vacua [26][27][28][29][30] as the first step toward vacua with small superpotentials [31].…”

A counterexample to the Nelson-Seiberg theorem

“…It is then unnatural to turn on JHEP10(2020)072 only R-symmetric fluxes and obtain an R-symmetric effective superpotential. Our model does not affect the accuracy of the field counting method if we only consider R-symmetric SUSY vacua in the third branch, or string vacua with enhanced symmetries [40][41][42][43][44]. A recent exploration of new counterexamples [45] shows that such R-symmetry breaking feature of SUSY vacua is common in all currently known constructions.…”

Purely non-perturbative AdS vacua and the swampland

“…Therefore our model is valid for any value of h 1,1 with the understanding that h 1,1 − 1 number of Kähler moduli are fixed by the choice of complex moduli in a Minkowski vacuum. Models with Minkowski vacuum W 0 = 0 were also recently considered in [31] and [32] by pursuing the ideas originally proposed in [33] to restrict the set of complex deformations to an algebraic set which satisfies W 0 = 0. In particular, [32] consider an F-theory compactification on K3 × K3 which implies a pretty large value for h 1,1 , it would be interesting to see how to explicitly fix all but one of the Kähler deformations as a function of complex deformation and follow up with our superpotential (1).…”