Systematics of Axion Inflation in Calabi-Yau Hypersurfaces

TL;DR

This paper systematically studies axion inflation in type IIB string theory compactifications on Calabi-Yau hypersurfaces, computing moduli space metrics and axion charges to bound the inflationary field range and assess alignment effects.

Contribution

It provides the first comprehensive survey of axion inflation constraints in Calabi-Yau hypersurfaces with detailed calculations of moduli space metrics and charge matrices, establishing upper bounds on field ranges.

Findings

Field range bound: Δφ ≲ 0.3 M_pl without monodromy.

Maximum alignment factor: approximately 2.6.

Analysis extended to threefolds with h^{1,1} up to 100.

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 K\"ahler 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 $\Delta \phi$ that results from the leading instanton potential, in the absence of monodromy. The bound on the field range in this ensemble is $\Delta \phi \lesssim 0.3 M_{\rm{pl}}$, in a compactification where the smallest curve volume is $(2\pi)^2\alpha'$, 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.