Aspects of canonical differential equations for Calabi-Yau geometries and beyond
Abstract We show how a method to construct canonical differential equations for multi-loop Feynman integrals recently introduced by some of the authors can be extended to cases where the associated geometry is of Calabi-Yau type and even beyond. This can be achieved by supplementing the method with...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)128 |
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| author | Claude Duhr Sara Maggio Christoph Nega Benjamin Sauer Lorenzo Tancredi Fabian J. Wagner |
| author_facet | Claude Duhr Sara Maggio Christoph Nega Benjamin Sauer Lorenzo Tancredi Fabian J. Wagner |
| author_sort | Claude Duhr |
| collection | DOAJ |
| description | Abstract We show how a method to construct canonical differential equations for multi-loop Feynman integrals recently introduced by some of the authors can be extended to cases where the associated geometry is of Calabi-Yau type and even beyond. This can be achieved by supplementing the method with information from the mixed Hodge structure of the underlying geometry. We apply these ideas to specific classes of integrals whose associated geometry is a one-parameter family of Calabi-Yau varieties, and we argue that the method can always be successfully applied to those cases. Moreover, we perform an in-depth study of the properties of the resulting canonical differential equations. In particular, we show that the resulting canonical basis is equivalent to the one obtained by an alternative method recently introduced in the literature. We apply our method to non-trivial and cutting-edge examples of Feynman integrals necessary for gravitational wave scattering, further showcasing its power and flexibility. |
| format | Article |
| id | doaj-art-4e572b2c83a44fedb4ea92ab1c63b65e |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-4e572b2c83a44fedb4ea92ab1c63b65e2025-08-20T03:42:43ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025619110.1007/JHEP06(2025)128Aspects of canonical differential equations for Calabi-Yau geometries and beyondClaude Duhr0Sara Maggio1Christoph Nega2Benjamin Sauer3Lorenzo Tancredi4Fabian J. Wagner5Bethe Center for Theoretical Physics, Universität BonnBethe Center for Theoretical Physics, Universität BonnPhysics Department, TUM School of Natural Sciences, Technical University of MunichInstitut für Physik, Humboldt-Universität zu BerlinPhysics Department, TUM School of Natural Sciences, Technical University of MunichPhysics Department, TUM School of Natural Sciences, Technical University of MunichAbstract We show how a method to construct canonical differential equations for multi-loop Feynman integrals recently introduced by some of the authors can be extended to cases where the associated geometry is of Calabi-Yau type and even beyond. This can be achieved by supplementing the method with information from the mixed Hodge structure of the underlying geometry. We apply these ideas to specific classes of integrals whose associated geometry is a one-parameter family of Calabi-Yau varieties, and we argue that the method can always be successfully applied to those cases. Moreover, we perform an in-depth study of the properties of the resulting canonical differential equations. In particular, we show that the resulting canonical basis is equivalent to the one obtained by an alternative method recently introduced in the literature. We apply our method to non-trivial and cutting-edge examples of Feynman integrals necessary for gravitational wave scattering, further showcasing its power and flexibility.https://doi.org/10.1007/JHEP06(2025)128Differential and Algebraic GeometryScattering AmplitudesHigher-Order Perturbative Calculations |
| spellingShingle | Claude Duhr Sara Maggio Christoph Nega Benjamin Sauer Lorenzo Tancredi Fabian J. Wagner Aspects of canonical differential equations for Calabi-Yau geometries and beyond Journal of High Energy Physics Differential and Algebraic Geometry Scattering Amplitudes Higher-Order Perturbative Calculations |
| title | Aspects of canonical differential equations for Calabi-Yau geometries and beyond |
| title_full | Aspects of canonical differential equations for Calabi-Yau geometries and beyond |
| title_fullStr | Aspects of canonical differential equations for Calabi-Yau geometries and beyond |
| title_full_unstemmed | Aspects of canonical differential equations for Calabi-Yau geometries and beyond |
| title_short | Aspects of canonical differential equations for Calabi-Yau geometries and beyond |
| title_sort | aspects of canonical differential equations for calabi yau geometries and beyond |
| topic | Differential and Algebraic Geometry Scattering Amplitudes Higher-Order Perturbative Calculations |
| url | https://doi.org/10.1007/JHEP06(2025)128 |
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