Heavy Tails in Calabi-Yau Moduli Spaces

Abstract

We study the statistics of the metric on Kähler moduli space in compactifications of string theory on Calabi-Yau hypersurfaces in toric varieties. We find striking hierarchies in the eigenvalues of the metric and of the Riemann curvature contribution to the Hessian matrix: both spectra display heavy tails. The curvature contribution to the Hessian is non-positive, suggesting a reduced probability of metastability compared to cases in which the derivatives of the Kähler potential are uncorrelated. To facilitate our analysis, we have developed a novel triangulation algorithm that allows efficient study of hypersurfaces with $h^{1,1}$ as large as 25, which is difficult using algorithms internal to packages such as Sage. Our results serve as input for statistical studies of the vacuum structure in flux compactifications, and of the distribution of axion decay constants in string theory.

48 pages, 28 figures

References in corpus (4)

• On the Geometry of the String Landscape and the Swampland
• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
• Moduli Stabilisation and Applications in IIB String Theory

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• A search for ultra-light axions using precision cosmological data
• On the Possibility of Large Axion Moduli Spaces
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• D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
• A landscape of orientifold vacua
• Perturbative Stability along the Supersymmetric Directions of the Landscape
• Spectral statistics for the difference of two Wishart matrices