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Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces.
- Source :
-
Journal of High Energy Physics . Jul2023, Vol. 2023 Issue 7, p1-49. 49p. - Publication Year :
- 2023
-
Abstract
- We give the first numerical calculation of the spectrum of the Laplacian acting on bundle-valued forms on a Calabi-Yau three-fold. Specifically, we show how to compute the approximate eigenvalues and eigenmodes of the Dolbeault Laplacian acting on bundle-valued (p, q)-forms on Kähler manifolds. We restrict our attention to line bundles over complex projective space and Calabi-Yau hypersurfaces therein. We give three examples. For two of these, ℙ3 and a Calabi-Yau one-fold (a torus), we compare our numerics with exact results available in the literature and find complete agreement. For the third example, the Fermat quintic three-fold, there are no known analytic results, so our numerical calculations are the first of their kind. The resulting spectra pass a number of non-trivial checks that arise from Serre duality and the Hodge decomposition. The outputs of our algorithm include all the ingredients one needs to compute physical Yukawa couplings in string compactifications. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 11266708
- Volume :
- 2023
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of High Energy Physics
- Publication Type :
- Academic Journal
- Accession number :
- 170391814
- Full Text :
- https://doi.org/10.1007/JHEP07(2023)164