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: Claude Duhr, Sara Maggio, Christoph Nega, Benjamin Sauer, Lorenzo Tancredi, Fabian J. Wagner
Format: Article
Language:English
Published: SpringerOpen 2025-06-01
Series:Journal of High Energy Physics
Subjects:
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.
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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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