Systematics of Axion Inflation in Calabi-Yau Hypersurfaces

TL;DR

The paper systematically analyzes axion inflation arising from Ramond–Ramond four-form axions in type IIB string theory on Calabi–Yau hypersurfaces within toric varieties. By computing the Kähler-moduli metric and the axion-charge matrix Q for all CY threefolds with h^{1,1} ≤ 4 in the Kreuzer–Skarke database and modeling leading instanton potentials without monodromy, the authors derive a robust upper bound Δφ ≲ 0.3 M_{ m pl} and identify a maximal alignment enhancement of about 2.6, with the strongest effects occurring at h^{1,1}=4. Extending the analysis to h^{1,1} ≤ 100 reveals that while alignment can produce sizable enhancements (η ≈ 7.86), the geometric field range remains sub-Planckian due to increasing Calabi–Yau volumes, and the axion-charge matrix Q typically contains a dominant identity block that limits large-field inflation in this setup. The work highlights how orientifold, brane, and flux effects could modify these conclusions and points to further avenues (e.g., D7-brane dynamics and nontrivial monodromy) for achieving larger field ranges within controlled regimes.

Abstract

We initiate a comprehensive survey of axion inflation in compactifications of type IIB string theory on Calabi-Yau hypersurfaces in toric varieties. For every threefold with $h^{1,1} \le 4$ in the Kreuzer-Skarke database, we compute the metric on Kähler moduli space, as well as the matrix of four-form axion charges of Euclidean D3-branes on rigid divisors. These charges encode the possibility of enlarging the field range via alignment. We then determine an upper bound on the inflationary field range $Δφ$ that results from the leading instanton potential, in the absence of monodromy. The bound on the field range in this ensemble is $Δφ\lesssim 0.3 M_{\rm{pl}}$, in a compactification where the smallest curve volume is $(2π)^2α'$, and we argue that the sigma model expansion is adequately controlled. The largest increase resulting from alignment is a factor $\approx 2.6$. We also examine a set of threefolds with $h^{1,1}$ up to $100$ and characterize their axion charge matrices. We discuss how our findings could be modified by the effects of orientifolding, seven-branes, and fluxes.

Figures (5)

• Figure 1: The geometric field range $\mathcal{R}$ is the semi-diameter of the fundamental domain $\mathcal{F}$, which is the region contained in the intersection of the $2P$ hyperplane constraints $-\pi \leq Q\indices{^a_i}\theta^i \leq \pi$. Surfaces of constant distance are ellipsoids with weight matrix $K_{ij}$.
• Figure 2: Histogram of geometric field ranges $\mathcal{R}$, in units of the reduced Planck mass $M_{\mathrm{pl}}$, for $h^{1,1} \leq 4$. The inset shows the tail of the distribution.
• Figure 3: Histogram of enhancements $\eta$ for $h^{1,1} = 2, 3, 4$. Inset demonstrates the large peak at $\eta = 1$, i.e. many geometries see no enhancement in size, or a reduction, from a non-trivial $Q$.
• Figure 4: $\log_{10}$ of the mean volumes ${\cal{V}}$ as a function of $h^{1,1}$.
• Figure 5: Average $\xi_N$ and $q_N$ at large $h^{1,1}$.