Mass Hierarchies and Scaling Scenarios for Perturbatively Flat Flux Vacua
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Within the setting type IIB string theory compactifications on a Calabi-Yau orientifold, we systematically analyze the scaling behavior of the superpotential W0 and the moduli masses with respect to the flux-induced tadpole charge Nflux. We do this for a set of explicit geometries in the large complex structure regime. In particular, we use a recipe proposed by Demirtas, Kim, McAllister, and Moritz (DKMM) in combination with a recent statistical analysis of Carta, Mininno, and Shukla (CMS) to solve the F -term equations for this set of geometries. We will go beyond the effective approach taken in this recipe, allowing us to explicitly compute the masses of the moduli. We furthermore stabilize a single Kähler modulus utilizing the KKLT- recipe. For all models investigated by CMS, we find that the bounding region of the distribution of W0 with respect to Nflux can be described by an exponential scaling. Furthermore, we find that the mass of the lightest modulus scales as a power law with respect to W0, indicating that smaller values of W0 give rise to lighter moduli. The most interesting finding is that the mass scale of the heaviest modulus competes with, or drastically exceeds, the Kaluza-Klein scale of the compactification for all of these models. We consequently compute the scaling of the ratio between the heaviest modulus and the Kaluza-Klein scale with respect to Nflux, indicating that these models need unrealistically large flux numbers in order to give a correct mass hierarchy. We extend the analysis to a handful of models with three complex structure moduli, one of which admits a flux vacuum with a correct mass hierarchy.