Moduli stabilization in type IIB orientifolds at h2,1 = 50

Abstract

We study moduli stabilization in Calabi-Yau orientifold compactifications of type IIB string theory with O3- and O7-planes. We consider a Calabi-Yau three-fold with Hodge number h2,1 = 50 and stabilize all axio-dilaton and complex-structure moduli by three-form fluxes. This is a challenging task, especially for large moduli-space dimensions. To address this question we develop an algorithm to generate 105 flux vacua with small flux number Nflux. Based on recent results by Crinò et al. we estimate the bound imposed by the tadpole-cancellation condition as Nflux≤ mathcal{O} (103), however, the smallest flux number we obtain in our search is of order Nflux = mathcal{O} (104). This implies, in particular, that for all solutions to the F-term equations in our data set the tadpole conjecture is satisfied.