Eigenvalues and eigenforms on Calabi-Yau threefolds

Abstract

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

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• Numerical Calabi-Yau metrics from holomorphic networks
• Calabi-Yau CFTs and Random Matrices
• Warp factor and the gravitational wave spectrum
• Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory $B-L$ MSSM