Abstract
We argue that super-Planckian diameters of axion fundamental domains can arise in Calabi-Yau compactifications of string theory. In a theory with N axions θ i, the fundamental domain is a polytope defined by the periodicities of the axions, via constraints of the form − π < Q i j θ j < π. We compute the diameter of the fundamental domain in terms of the eigenvalues f 21 ≤ … ≤ f 2 N of the metric on field space, and also, crucially, the largest eigenvalue of (QQ ⊤)−1. At large N, QQ ⊤ approaches a Wishart matrix, due to universality, and we show that the diameter is at least Nf N , exceeding the naive Pythagorean range by a factor > \( \sqrt{N} \). This result is robust in the presence of P > N constraints, while for P = N the diameter is further enhanced by eigenvector delocalization to N 3/2 f N . We directly verify our results in explicit Calabi-Yau compactifications of type IIB string theory. In the classic example with h 1,1 = 51 where parametrically controlled moduli stabilization was demonstrated by Denef et al. in [1], the largest metric eigenvalue obeys f N ≈ 0.013M pl. The random matrix analysis then predicts, and we exhibit, axion diameters ≈ M pl for the precise vacuum parameters found in [1]. Our results provide a framework for pursuing large-field axion inflation in well-understood flux vacua.
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Bachlechner, T.C., Long, C. & McAllister, L. Planckian axions in string theory. J. High Energ. Phys. 2015, 1–36 (2015). https://doi.org/10.1007/JHEP12(2015)042
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DOI: https://doi.org/10.1007/JHEP12(2015)042