Generalized hypergeometric functions and intersection theory for Feynman integrals

TL;DR

This paper introduces a novel application of intersection theory to construct a coaction on generalized hypergeometric functions, enabling a deeper understanding of Feynman integrals in dimensional regularization.

Contribution

It develops a new intersection theory-based method to analyze hypergeometric functions associated with Feynman integrals, reproducing known structures in dimensional regularization.

Findings

Constructed a coaction on generalized hypergeometric functions.

Reproduces coaction on multiple polylogarithms in dimensional regularization.

Provides a new mathematical framework for Feynman integral analysis.

Abstract

Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection theory. We propose a new application of intersection theory to construct a coaction on generalized hypergeometric functions. When applied to dimensionally regularized Feynman integrals, this coaction reproduces the coaction on multiple polylogarithms order by order in the parameter of dimensional regularization.