Feynman Integral Relations from GKZ Hypergeometric Systems

Henrik J. Munch

Feynman Integral Relations from GKZ Hypergeometric Systems

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arxiv 2207.09780 v1 pith:O2ZFZGVW submitted 2022-07-20 hep-th math-phmath.MP

Henrik J. Munch This is my paper

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abstract

We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic scales. Utilizing the GKZ system and its relation to $D$-module theory, we propose a novel method for obtaining differential equations for master integrals. This note is based on the longer manuscript arXiv:2204.12983.

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Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module
hep-th 2025-06 conditional novelty 6.0 of 10

A Griffiths-Dwork based algorithm builds annihilators and D-modules for Feynman-like integrals, and in all tested cases the holonomic rank matches the twisted de Rham cohomology dimension.

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