Abstract
We study the topological properties of Calabi-Yau threefold hypersurfaces at large h1,1. We obtain two million threefolds X by triangulating polytopes from the Kreuzer-Skarke list, including all polytopes with 240 ≤ h1,1 ≤ 491. We show that the Kähler cone of X is very narrow at large h1,1, and as a consequence, control of the α′ expansion in string compactifications on X is correlated with the presence of ultralight axions. If every effective curve has volume ≥ 1 in string units, then the typical volumes of irreducible effective curves and divisors, and of X itself, scale as (h1,1)p, with 3 ≲ p ≲ 7 depending on the type of cycle in question. Instantons from branes wrapping these cycles are thus highly suppressed.
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Demirtas, M., Long, C., McAllister, L. et al. The Kreuzer-Skarke axiverse. J. High Energ. Phys. 2020, 138 (2020). https://doi.org/10.1007/JHEP04(2020)138
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DOI: https://doi.org/10.1007/JHEP04(2020)138