Eigenvalues and eigenforms on Calabi–Yau threefolds
Copyright policy )Eigenvalues and eigenforms on Calabi–Yau threefolds
We present a numerical algorithm for computing the spectrum of the Laplace-de Rham operator on Calabi-Yau manifolds, extending previous work on the scalar Laplace operator. Using an approximate Calabi-Yau metric as input, we compute the eigenvalues and eigenforms of the Laplace operator acting on $(p,q)$-forms for the example of the Fermat quintic threefold. We provide a check of our algorithm by computing the spectrum of $(p,q)$-eigenforms on $\mathbb{P}^{3}$.
38 pages, 17 figures, 4 tables; v2: increased number of points in numerical integration; v3: updated plots, version submitted for peer review
- SORBONNE UNIVERSITE France
- Sorbonne University France
- Sorbonne Paris Cité France
- Sorbonne University France
- SORBONNE UNIVERSITE France
High Energy Physics - Theory, Mathematics - Differential Geometry, metric: Calabi-Yau, space: Calabi-Yau, eigenvalue problems on manifolds, FOS: Physical sciences, numerical metrics, [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], Calabi-Yau manifolds (algebro-geometric aspects), computational differential geometry, Computational methods for problems pertaining to differential geometry, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), Calabi-Yau manifolds, FOS: Mathematics, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], Spectral theory; eigenvalue problems on manifolds, Calabi-Yau theory (complex-analytic aspects), Laplace-de Rham operator, operator: Laplace
High Energy Physics - Theory, Mathematics - Differential Geometry, metric: Calabi-Yau, space: Calabi-Yau, eigenvalue problems on manifolds, FOS: Physical sciences, numerical metrics, [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], Calabi-Yau manifolds (algebro-geometric aspects), computational differential geometry, Computational methods for problems pertaining to differential geometry, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), Calabi-Yau manifolds, FOS: Mathematics, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], Spectral theory; eigenvalue problems on manifolds, Calabi-Yau theory (complex-analytic aspects), Laplace-de Rham operator, operator: Laplace
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