Numerical Metrics, Curvature Expansions and Calabi-Yau Manifolds

Abstract

We discuss the extent to which numerical techniques for computing approximations to Ricci-flat metrics can be used to investigate hierarchies of curvature scales on Calabi-Yau manifolds. Control of such hierarchies is integral to the validity of curvature expansions in string effective theories. Nevertheless, for seemingly generic points in moduli space it can be difficult to analytically determine if there might be a highly curved region localized somewhere on the Calabi-Yau manifold. We show that numerical techniques are rather efficient at deciding this issue.

arXiv comment14 pages, 8 figures

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• Machine Learning on generalized Complete Intersection Calabi-Yau Manifolds
• Chern-Simons Invariants and Heterotic Superpotentials
• Constructing and Machine Learning Calabi-Yau Five-folds
• Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory $B-L$ MSSM
• cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature
• Yukawa Textures From Singular Spectral Data