A Calabi-Yau-to-Curve Correspondence for Feynman Integrals
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912191331958784 |
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| author | Jockers, Hans Kotlewski, Sören Kuusela, Pyry McLeod, Andrew J. Pögel, Sebastian Sarve, Maik Wang, Xing Weinzierl, Stefan |
| author_facet | Jockers, Hans Kotlewski, Sören Kuusela, Pyry McLeod, Andrew J. Pögel, Sebastian Sarve, Maik Wang, Xing Weinzierl, Stefan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_05785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Calabi-Yau-to-Curve Correspondence for Feynman Integrals Jockers, Hans Kotlewski, Sören Kuusela, Pyry McLeod, Andrew J. Pögel, Sebastian Sarve, Maik Wang, Xing Weinzierl, Stefan High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry 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. |
| title | A Calabi-Yau-to-Curve Correspondence for Feynman Integrals |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry |
| url | https://arxiv.org/abs/2404.05785 |