A Calabi-Yau-to-curve correspondence for Feynman integrals
Abstract It has long been known that the maximal cut of the equal-mass four-loop banana integral is a period of a family of Calabi-Yau threefolds that depends on the kinematic variable z = m 2/p 2. We show that it can also be interpreted as a period of a family of genus-two curves. We do this by int...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2025)030 |
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| Summary: | Abstract It has long been known that the maximal cut of the equal-mass four-loop banana integral is a period of a family of Calabi-Yau threefolds that depends on the kinematic variable z = m 2/p 2. We show that it can also be interpreted as a period of a family of genus-two curves. We do this by introducing a general Calabi-Yau-to-curve correspondence, which in this case locally relates the original period of the family of Calabi-Yau threefolds to a period of a family of genus-two curves that varies holomorphically with the kinematic variable z. In addition to working out the concrete details of this correspondence for the equal-mass four-loop banana integral, we outline when we expect a correspondence of this type to hold. |
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| ISSN: | 1029-8479 |