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 $h^{1,1} \le 4$ 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.