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Aspects of canonical differential equations for Calabi-Yau geometries and beyond

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arxiv 2503.20655 v1 pith:TPUOR6G3 submitted 2025-03-26 hep-th hep-phmath.AG

classification hep-thhep-phmath.AG
keywords methodcanonicalcalabi-yaudifferentialequationsgeometryintegralsapply
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 5 Pith papers

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