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arXiv · 1808.01282

The Kreuzer-Skarke Axiverse

Mehmet Demirtas·Cody Long·Liam McAllister·Mike Stillman
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Abstract

We study the topological properties of Calabi-Yau threefold hypersurfaces at large $h^{1,1}$. We obtain two million threefolds $X$ by triangulating polytopes from the Kreuzer-Skarke list, including all polytopes with $240 \le h^{1,1}\le 491$. We show that the K\"ahler cone of $X$ is very narrow at large $h^{1,1}$, and as a consequence, control of the $\alpha^{\prime}$ expansion in string compactifications on $X$ is correlated with the presence of ultralight axions. If every effective curve has volume $\ge 1$ in string units, then the typical volumes of irreducible effective curves and divisors, and of $X$ itself, scale as $(h^{1,1})^p$, with $3\lesssim p \lesssim 7$ depending on the type of cycle in question. Instantons from branes wrapping these cycles are thus highly suppressed.

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Mehmet Demirtas, Cody Long, Liam McAllister, Mike Stillman. 2018-08-03. The Kreuzer-Skarke Axiverse. https://arxiv.org/abs/1808.01282

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