Aspects of canonical differential equations for Calabi-Yau geometries and beyond
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916663083925504 |
|---|---|
| author | Duhr, Claude Maggio, Sara Nega, Christoph Sauer, Benjamin Tancredi, Lorenzo Wagner, Fabian J. |
| author_facet | Duhr, Claude Maggio, Sara Nega, Christoph Sauer, Benjamin Tancredi, Lorenzo Wagner, Fabian J. |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Aspects of canonical differential equations for Calabi-Yau geometries and beyond Duhr, Claude Maggio, Sara Nega, Christoph Sauer, Benjamin Tancredi, Lorenzo Wagner, Fabian J. High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry 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. |
| title | Aspects of canonical differential equations for Calabi-Yau geometries and beyond |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry |
| url | https://arxiv.org/abs/2503.20655 |