Picard-Fuchs Equations of Twisted Differential forms associated to 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.

21 pages. This text is a contribution to the proceedings of the conference Regulators V, 3-13 juin 2024, Department of Mathematics, University of Pisa, Italy. Version to the published by the AMS in the Contemporary Mathematics series