The Kreuzer-Skarke Axiverse

TL;DR

The paper surveys Calabi–Yau threefold hypersurfaces with large $h^{1,1}$ by generating millions of examples from the Kreuzer–Skarke list via FRST triangulations, then bounds the Kähler cone using ambient toric data and a stretched Kähler cone framework. It demonstrates that the Kähler cone becomes very narrow at large $h^{1,1}$, linking controlled $\alpha'$ expansions to the presence of ultralight axions, and shows cycle volumes grow as a power $(h^{1,1})^p$ (with $3\lesssim p\lesssim7$), suppressing instantons. The study derives upper bounds on axion masses and geometric field ranges, finding an axiverse with hundreds of axions, many effectively massless with sub-Planckian field ranges, and discusses implications for axion cosmology and potential large-field inflation in limited cases. It also documents significant computational challenges and proposes future work to refine the geometric data and explore nonholomorphic instanton effects.

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 Kähler cone of $X$ is very narrow at large $h^{1,1}$, and as a consequence, control of the $α^{\prime}$ 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.

Figures (10)

• Figure 1: Number of nonzero entries of $\kappa_{ABC}$, cf. \ref{['intnumberdef']}, vs. $h^{1,1}$.
• Figure 2: Root mean square size of nonzero entries of $\kappa_{ABC}$ vs. $h^{1,1}$.
• Figure 3: $\cos (\theta_{\text{min}})$, defined in (\ref{['eq:minang']}), vs. $h^{1,1}$.
• Figure 4: $\log_{10}(\text{d}_{\text{min}}^V)$, defined in \ref{['eq:dminV']}, vs. $h^{1,1}$ and vs. $\log_{10}(h^{1,1})$. The fit is $\log_{10}(\text{d}_{\text{min}}^V)= -1.7 + 3.1 \log_{10} (h^{1,1})$.
• Figure 5: $\log_{10}(\text{d}_{\text{min}}^\cap)$, defined in \ref{['eq:dminint']}, vs. $\log_{10}(h^{1,1})$. The fit is $\log_{10}(\text{d}_{\text{min}}^\cap)= -1.4 + 2.5 \log_{10}(h^{1,1})$.