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Systematics of axion inflation in Calabi-Yau hypersurfaces. (English) Zbl 1377.85019
Summary: 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 \(h^{1,1} \leq 4\) 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 \(\Delta \phi\) that results from the leading instanton potential, in the absence of monodromy. The bound on the field range in this ensemble is \(\Delta \phi < 0.3 M_{Pl}\), 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. 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 \(h^{1,1}\). Furthermore, we find that many toric divisors are rigid – and the corresponding charge matrices are relatively trivial – at large \(h^{1,1}\). 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.

MSC:
85A40 Cosmology
83F05 Cosmology
53B35 Local differential geometry of Hermitian and Kählerian structures
81T60 Supersymmetric field theories in quantum mechanics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
83E30 String and superstring theories in gravitational theory
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