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This research aims to extend a pole reduction algorithm to derive differential operators associated with Feynman integrals.

April 17, 2026Open Access

Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals

Key Points

This research aims to extend a pole reduction algorithm to derive differential operators associated with Feynman integrals.
Applied the Griffiths-Dwork pole reduction algorithm.
Derived D-modules of differential operators.
Examined twisted Picard-Fuchs operators for specific differential motives.
Presented new twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives.
Illustrated the effective computation of twisted period integrals from Feynman integrals.

Abstract

Dimensionally or analytically regulated Feynman integrals lead to relative twisted period integrals. We present a recent extension of the Griffiths-Dwork pole reduction algorithm for deriving the D-module of differential operators acting on the twisted differential forms from Feynman integrals. We illustrate the application of this algorithm by providing twisted Picard-Fuchs operators for hypergeometric, elliptic and Calabi-Yau differential motives arising from families of Feynman integrals.

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Pierre Vanhove

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Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals

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