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

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 h(2,1) = 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 10(5) flux vacua with small flux number N-flux. Based on recent results by Crino et al. we estimate the bound imposed by the tadpole-cancellation condition as N-flux <= O(10(3)), however, the smallest flux number we obtain in our search is of order N-flux = O(10(4)). This implies, in particular, that for all solutions to the F-term equations in our data set the tadpole conjecture is satisfied.

Automated summary

In this article, we study the moduli stabilization in Calabi-Yau orientifold compactifications of type IIB string theory with O3- and O7-planes. By using three-form fluxes, we stabilize all axio-dilaton and complex-structure moduli for a Calabi-Yau three-fold with Hodge number h(2,1) = 50. To address this issue, we develop an algorithm to generate 10(5) flux vacua with small flux number N-flux. Based on recent results, we estimate the bound imposed by the tadpole-cancellation condition as N-flux <= O(10(3)), but the smallest flux number we obtain in our search is of order N-flux = O(10(4)). This implies that the tadpole conjecture is satisfied for all solutions to the F-term equations in our data set.