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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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)030 |
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| author | Hans Jockers Sören Kotlewski Pyry Kuusela Andrew J. McLeod Sebastian Pögel Maik Sarve Xing Wang Stefan Weinzierl |
| author_facet | Hans Jockers Sören Kotlewski Pyry Kuusela Andrew J. McLeod Sebastian Pögel Maik Sarve Xing Wang Stefan Weinzierl |
| author_sort | Hans Jockers |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d15275dca4f14f958508bd54bfc96fef |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d15275dca4f14f958508bd54bfc96fef2025-01-19T12:07:09ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025116410.1007/JHEP01(2025)030A Calabi-Yau-to-curve correspondence for Feynman integralsHans Jockers0Sören Kotlewski1Pyry Kuusela2Andrew J. McLeod3Sebastian Pögel4Maik Sarve5Xing Wang6Stefan Weinzierl7PRISMA+ Cluster of Excellence, Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität MainzPRISMA+ Cluster of Excellence, Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität MainzPRISMA+ Cluster of Excellence, Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität MainzHiggs Centre for Theoretical Physics, School of Physics and Astronomy, The University of EdinburghPRISMA+ Cluster of Excellence, Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität MainzPRISMA+ Cluster of Excellence, Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität MainzPhysik Department, TUM School of Natural Sciences, Technische Universität MünchenPRISMA+ Cluster of Excellence, Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität MainzAbstract 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.https://doi.org/10.1007/JHEP01(2025)030Scattering AmplitudesDifferential and Algebraic Geometry |
| spellingShingle | Hans Jockers Sören Kotlewski Pyry Kuusela Andrew J. McLeod Sebastian Pögel Maik Sarve Xing Wang Stefan Weinzierl A Calabi-Yau-to-curve correspondence for Feynman integrals Journal of High Energy Physics Scattering Amplitudes Differential and Algebraic Geometry |
| title | A Calabi-Yau-to-curve correspondence for Feynman integrals |
| title_full | A Calabi-Yau-to-curve correspondence for Feynman integrals |
| title_fullStr | A Calabi-Yau-to-curve correspondence for Feynman integrals |
| title_full_unstemmed | A Calabi-Yau-to-curve correspondence for Feynman integrals |
| title_short | A Calabi-Yau-to-curve correspondence for Feynman integrals |
| title_sort | calabi yau to curve correspondence for feynman integrals |
| topic | Scattering Amplitudes Differential and Algebraic Geometry |
| url | https://doi.org/10.1007/JHEP01(2025)030 |
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