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arXiv · 2204.12983

Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers

Vsevolod Chestnov·Federico Gasparotto·Manoj K. Mandal·Pierpaolo Mastrolia·Saiei J. Matsubara-Heo·Henrik J. Munch·Nobuki Takayama
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Abstract

We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose a novel, more efficient algorithm to compute Macaulay matrices, which are used to derive Pfaffian systems of differential equations. The Pfaffian matrices are then employed to obtain linear relations for ${\cal A}$-hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.

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Vsevolod Chestnov, Federico Gasparotto, Manoj K. Mandal, Pierpaolo Mastrolia, Saiei J. Matsubara-Heo, Henrik J. Munch, Nobuki Takayama. 2022-04-27. Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers. https://doi.org/10.1007/jhep09(2022)187

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