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

TL;DR

This paper extends the Griffiths-Dwork pole reduction algorithm to derive Picard-Fuchs equations for twisted differential forms related to Feynman integrals, covering hypergeometric, elliptic, and Calabi-Yau cases.

Contribution

It introduces an advanced algorithm for computing D-modules of differential operators acting on twisted forms from Feynman integrals, applicable to complex geometric motives.

Findings

Derived twisted Picard-Fuchs operators for various Feynman integral families.

Extended the Griffiths-Dwork pole reduction algorithm for twisted forms.

Applied the method to hypergeometric, elliptic, and Calabi-Yau motives.

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.