Level crossings, attractor points and complex multiplication
Abstract We study the complex structure moduli dependence of the scalar Laplacian eigenmodes for one-parameter families of Calabi-Yau n-folds in ℙ n+1. It was previously observed that some eigenmodes get lighter while others get heavier as a function of these moduli, which leads to eigenvalue crossi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2023)164 |
| _version_ | 1797675807240355840 |
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| author | Hamza Ahmed Fabian Ruehle |
| author_facet | Hamza Ahmed Fabian Ruehle |
| author_sort | Hamza Ahmed |
| collection | DOAJ |
| description | Abstract We study the complex structure moduli dependence of the scalar Laplacian eigenmodes for one-parameter families of Calabi-Yau n-folds in ℙ n+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. |
| first_indexed | 2024-03-11T22:20:04Z |
| format | Article |
| id | doaj.art-847f06a689b847028b6981705cb6e7cd |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T22:20:04Z |
| publishDate | 2023-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-847f06a689b847028b6981705cb6e7cd2023-09-24T11:07:00ZengSpringerOpenJournal of High Energy Physics1029-84792023-06-012023613010.1007/JHEP06(2023)164Level crossings, attractor points and complex multiplicationHamza Ahmed0Fabian Ruehle1Department of Physics, Northeastern UniversityDepartment of Physics, Northeastern UniversityAbstract We study the complex structure moduli dependence of the scalar Laplacian eigenmodes for one-parameter families of Calabi-Yau n-folds in ℙ n+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.https://doi.org/10.1007/JHEP06(2023)164Black Holes in String TheoryString and Brane PhenomenologySuperstring Vacua |
| spellingShingle | Hamza Ahmed Fabian Ruehle Level crossings, attractor points and complex multiplication Journal of High Energy Physics Black Holes in String Theory String and Brane Phenomenology Superstring Vacua |
| title | Level crossings, attractor points and complex multiplication |
| title_full | Level crossings, attractor points and complex multiplication |
| title_fullStr | Level crossings, attractor points and complex multiplication |
| title_full_unstemmed | Level crossings, attractor points and complex multiplication |
| title_short | Level crossings, attractor points and complex multiplication |
| title_sort | level crossings attractor points and complex multiplication |
| topic | Black Holes in String Theory String and Brane Phenomenology Superstring Vacua |
| url | https://doi.org/10.1007/JHEP06(2023)164 |
| work_keys_str_mv | AT hamzaahmed levelcrossingsattractorpointsandcomplexmultiplication AT fabianruehle levelcrossingsattractorpointsandcomplexmultiplication |