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 h1,1≤ 12. In particular, we compute orientifold configurations for all favourable FRSTs for h1,1≤ 7, while randomly sampling triangulations for each pair of Hodge numbers up to h1,1 = 12. We find explicit string compactifications on these orientifolded Calabi-Yaus for which the D3-charge contribution coming from Op-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 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 left({h}_{+}^{1,1},{h}_{-}^{1,2}right) = (11, 491) with D3-brane charges |QD3| = 504 for the local D7 case and |QD3| = 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 the following link https://github.com/AndreasSchachner/CY_Orientifold_database.