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Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning

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arxiv 2012.04656 v2 pith:UJZGUCMO submitted 2020-12-08 hep-th

Lara B. Anderson , Mathis Gerdes , James Gray , Sven Krippendorf , Nikhil Raghuram , Fabian Ruehle This is my paper · ORCID
classification hep-th
keywords structuremetricscalabi-yaulearningmachinecrucialmethodsstring
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in $\mathbb{P}^4.$

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Forward citations

Cited by 7 Pith papers

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

  1. Warped Numerical Calabi-Yau Metrics

    hep-th 2026-07 conditional novelty 7.0 of 10

    First numerical GKP warped Type IIB flux background on a Dwork quintic, giving a 0.5% throat-volume estimate near the conifold and new metric/harmonic-form/warp-factor techniques.

  2. Balanced Metrics Know About SYZ

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    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.

  3. Machine Learning Free Quotients of CICYs

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  4. 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.

  5. Pre-Strings Lectures on Artificial Intelligence

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

  6. 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

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

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    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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