Feynman Integral Relations from GKZ Hypergeometric Systems

TL;DR

This paper introduces a new method for deriving differential equations for Feynman integrals by leveraging GKZ hypergeometric systems and their connection to $D$-module theory, applicable across various loop and scale configurations.

Contribution

It presents a novel approach that uses GKZ hypergeometric systems to analyze Feynman integrals, expanding the mathematical tools available for their study.

Findings

Derived differential equations for master integrals using GKZ systems

Unified framework for Feynman integrals across multiple loops and scales

Connection established between Feynman integrals and $D$-module theory

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.