Gluing via Intersection Theory

TL;DR

This paper introduces a novel intersection theory approach to analytically compute residues in the gluing process of planar one-loop five-point functions in N=4 super Yang-Mills theory, enhancing understanding of integrability methods.

Contribution

It develops a new intersection theory-based method to derive differential equations for residues in the gluing of Feynman graphs, advancing analytical techniques in supersymmetric gauge theories.

Findings

Derived canonical differential equations for residues

Revealed the twisted period nature of integral functions

Provided explicit solutions to the gluing residues

Abstract

Higher-point functions in N = 4 super Yang-Mills theory can be constructed using integrability by triangulating the surfaces on which Feynman graphs would be drawn. It remains hard to analytically compute the necessary re-gluing of the tiles by virtual particles. We propose a new approach to study a series of residues encountered in the two-particle gluing of the planar one-loop five-point function of stress tensor multiplets. After exposing the twisted period nature of the integral functions, we employ intersection theory to derive canonical differential equations and present a solution.