Modular Calabi-Yau Fourfolds and Connections to M-Theory Fluxes
| Autor: | Jockers, Hans, Kotlewski, Sören, Kuusela, Pyry |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this work, we study the local zeta functions of Calabi-Yau fourfolds. This is done by developing arithmetic deformation techniques to compute the factor of the zeta function that is attributed to the horizontal four-form cohomology. This, in turn, is sensitive to the complex structure of the fourfold. Focusing mainly on examples of fourfolds with a single complex structure parameter, it is demonstrated that the proposed arithmetic techniques are both applicable and consistent. We present a Calabi-Yau fourfold for which a factor of the horizontal four-form cohomology further splits into two pieces of Hodge type $(4,0)+(2,2)+(0,4)$ and $(3,1)+(1,3)$. The latter factor corresponds to a weight-3 modular form, which allows expressing the value of the periods in terms of critical values of the L-function of this modular form, in accordance with Deligne's conjecture. The arithmetic considerations are related to M-theory Calabi-Yau fourfold compactifications with background four-form fluxes. We classify such background fluxes according to their Hodge type. For those fluxes associated to modular forms, we express their couplings in the low-energy effective action in terms of L-function values. Comment: 77 pages, 6 figures. v2: physical interpretation of modular solutions corrected, minor clarifications added, references added. v3: appendix on modular form periods added |
| Databáze: | arXiv |
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