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Numerical Calabi-Yau metrics

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arxiv hep-th/0612075 v1 pith:2P7MMCEZ submitted 2006-12-11 hep-th

Michael R. Douglas , Robert L. Karp , Sergio Lukic , Rene Reinbacher This is my paper
classification hep-th
keywords metricscalabi-yaumethodsnumericalapproachapproximatingbalancedbuilds
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We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics, and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Balanced Metrics Know About SYZ

    hep-th 2026-07 conditional novelty 6.0 of 10

    Ambient balanced metric coefficients on Calabi-Yau manifolds decay as |ψ|^{-f(α)} near the large complex structure limit, and the exponent function's Legendre transform gives the dual tropical potential expected from SYZ.

  2. Approximate Ricci-flat Metrics for Calabi-Yau Manifolds

    hep-th 2025-06 conditional novelty 6.0 of 10

    Analytic approximate Ricci-flat Kähler potentials are obtained for one-parameter Dwork quintic and bi-cubic Calabi-Yau three-folds by fitting Donaldson's Ansatz to machine-learned numerical metrics.

  3. Pre-Strings Lectures on Artificial Intelligence

    hep-th 2026-07 accept novelty 5.5 of 10

    Lecture notes define neural-network field theory and survey how it recovers known QFT/string results plus applied AI techniques for string problems.

  4. Reproducing Standard Model Fermion Masses and Mixing in String Theory: A Heterotic Line Bundle Study

    hep-th 2025-07 conditional novelty 5.0 of 10

    Explicit heterotic line bundle models on a Calabi-Yau threefold are fitted to reproduce Standard Model quark and charged lepton masses and CKM mixing.

  5. What to do with a Ricci-flat Calabi--Yau metric?

    hep-th 2026-05 unverdicted novelty 3.0 of 10

    Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.

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