The Kreuzer-Skarke Axiverse

TL;DR

This study analyzes the topological features of a large class of Calabi-Yau threefolds, revealing how their geometric properties influence string compactification and the presence of ultralight axions.

Contribution

It provides a comprehensive dataset of two million Calabi-Yau threefolds and uncovers the relationship between their Kähler cone geometry and axion physics in string theory.

Findings

Kähler cone is very narrow at large h^{1,1}

Control of α' expansion correlates with ultralight axions

Cycle volumes scale polynomially with h^{1,1} depending on cycle type

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.