A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles

Abstract

The classification of 4D reflexive polytopes by Kreuzer and Skarke allows for a systematic construction of Calabi-Yau hypersurfaces as fine, regular, star triangulations (FRSTs). Until now, the vastness of this geometric landscape remains largely unexplored. In this paper, we construct Calabi-Yau orientifolds from holomorphic reflection involutions of such hypersurfaces with Hodge numbers $h^{1,1}\le 12$. In particular, we compute orientifold configurations for all favourable FRSTs for $h^{1,1}\le 7$, while randomly sampling triangulations for each pair of Hodge numbers up to $h^{1,1}=12$. We find explicit string compactifications on these orientifolded Calabi-Yaus for which the D3-charge contribution coming from O$p$-planes grows linearly with the number of complex structure and Kähler moduli. We further consider non-local D7-tadpole cancellation through Whitney branes. We argue that this leads to a significant enhancement of the total D3-tadpole as compared to conventional $\mathrm{SO}(8)$ stacks with $(4+4)$ D7-branes on top of O7-planes. In particular, before turning-on worldvolume fluxes, we find that the largest D3-tadpole in this class occurs for Calabi-Yau threefolds with $(h_{+}^{1,1},h_{-}^{1,2})=(11,491)$ with D3-brane charges $|Q_{\text{D3}}|=504$ for the local D7 case and $|Q_{\text{D3}}|=6,664$ for the non-local Whitney branes case, which appears to be large enough to cancel tadpoles and allow fluxes to stabilise all complex structure moduli. Our data is publicly available under http://github.com/AndreasSchachner/CY_Orientifold_database .

30 pages plus appendices, 5 figures

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