Moduli stabilization in type IIB orientifolds at $h^{2,1}=50$

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 $h^{2,1}=50$ 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 $N_{\mathrm{flux}}$. Based on recent results by Crinò et al. we estimate the bound imposed by the tadpole-cancellation condition as $N_{\mathrm{flux}}\le \mathcal{O}(10^3)$, however, the smallest flux number we obtain in our search is of order $N_{\mathrm{flux}}=\mathcal{O}(10^4)$. This implies, in particular, that for all solutions to the F-term equations in our data set the tadpole conjecture is satisfied.

21 pages, 3 figures; v2: minor changes and clarifications added, data set provided as ancillary files

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• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Bounds on complex structure moduli values for perturbative control