Planckian Axions in String Theory

Thomas C. Bachlechner; Cody Long; Liam McAllister

doi:10.1007/JHEP12(2015)042

paper

Planckian Axions in String Theory

arXiv:1412.1093 · doi:10.1007/JHEP12(2015)042

Abstract

We argue that super-Planckian diameters of axion fundamental domains can naturally 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 $- π < Q_{j}^{i} θ^{j} < π$ . We compute the diameter of the fundamental domain in terms of the eigenvalues $f_{1}^{2} \leq . ˙ . \leq f_{N}^{2}$ of the metric on field space, and also, crucially, the largest eigenvalue of $(Q Q^{⊤})^{- 1}$ . At large $N$ , $Q Q^{⊤}$ approaches a Wishart matrix, due to universality, and we show that the diameter is at least $N f_{N}$ , exceeding the naive Pythagorean range by a factor $> N$ . 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 $f_{N} \approx 0.013 M_{pl}$ . 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 achieving large-field axion inflation in well-understood flux vacua.

42 pages, 4 figures

Planckian Axions in String Theory

Abstract

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