CYJAX: A package for Calabi-Yau metrics with JAX

Gerdes, Mathis; Krippendorf, Sven

doi:10.1088/2632-2153/acdc84

Cited by 9 publications

(1 citation statement)

References 24 publications

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“…As already mentioned there are two other open-source packages, MLgeometry [DLQ20] and cyjax [GK22], that also may be used to predict CY metrics. These packages are similar to cymetric in that they use fully connected neural networks, trained by stochastic gradient descent.…”

Section: Outlook and Open Problemsmentioning

confidence: 99%

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

Anderson

Gerdes²,

Gray

et al. 2021

J. High Energ. Phys.

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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 ℙ4.

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Section: Outlook and Open Problemsmentioning

confidence: 99%

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

Anderson

Gerdes²,

Gray

et al. 2021

J. High Energ. Phys.

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show abstract

Moduli Stabilization in String Theory

McAllister,

Quevedo

2024

Handbook of Quantum Gravity

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Level crossings, attractor points and complex multiplication

Ahmed

Ruehle

2023

J. High Energ. Phys.

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We study the complex structure moduli dependence of the scalar Laplacian eigenmodes for one-parameter families of Calabi-Yau n-folds in ℙn+1. It was previously observed that some eigenmodes get lighter while others get heavier as a function of these moduli, which leads to eigenvalue crossing. We identify the cause for this behavior for the torus. We then show that at points in a sublocus of complex structure moduli space where Laplacian eigenmodes cross, the torus has complex multiplication. We speculate that the generalization to arbitrary Calabi-Yau manifolds could be that level crossing is related to rank one attractor points. To test this, we compute the eigenmodes numerically for the quartic K3 and the quintic threefold, and match crossings to CM and attractor points in these varieties. To quantify the error of our numerical methods, we also study the dependence of the numerical spectrum on the quality of the Calabi-Yau metric approximation, the number of points sampled from the Calabi-Yau variety, the truncation of the eigenbasis, and the distance from degeneration points in complex structure moduli space.

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CYJAX: A package for Calabi-Yau metrics with JAX

Cited by 9 publications

References 24 publications

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

Moduli Stabilization in String Theory

Level crossings, attractor points and complex multiplication

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