Systematics of axion inflation in Calabi-Yau hypersurfaces

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 h1,1 ≤ 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 ≲ 0.3Mpl, 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 ≈ 2.6. We also examine a set of threefolds with h1,1 up to 100 and characterize their axion charge matrices. While we find modest alignment in this ensemble, the maximum field range is ultimately suppressed by the volume of the internal space, which typically grows quickly with h1,1. Furthermore, we find that many toric divisors are rigid — and the corresponding charge matrices are relatively trivial — at large h1,1. It is therefore challenging to realize alignment via superpotentials generated only by Euclidean D3-branes, without taking into account the effects of flux, D7-branes, and orientifolding.