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Gluing via Intersection Theory.

Giulio Crisanti1,2, Burkhard Eden3, Maximilian Gottwald3

  • 1INFN, Sezione di Padova, Università degli Studi di Padova, Dipartimento di Fisica e Astronomia, Via Marzolo 8, I-35131 Padova, Italy and , Via Marzolo 8, I-35131 Padova, Italy.

Physical Review Letters
|July 31, 2025
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Summary
This summary is machine-generated.

Researchers developed a new method to calculate complex functions in N=4 super Yang-Mills theory. This approach uses integrability and intersection theory to solve challenges in analytically computing Feynman graphs for quantum field theory.

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Area of Science:

  • High Energy Physics
  • Quantum Field Theory
  • String Theory

Background:

  • Integrability methods are used to construct higher-point functions in N=4 super Yang-Mills theory by triangulating surfaces.
  • Analytical computation of Feynman graphs, particularly the regluing of components by virtual particles, remains a significant challenge.

Purpose of the Study:

  • To propose a novel approach for studying residues in the two-particle gluing of planar one-loop five-point functions of stress tensor multiplets.
  • To address the difficulties in analytically computing these complex functions.

Main Methods:

  • Utilizing integrability techniques for constructing higher-point functions.
  • Employing triangulation of surfaces for Feynman graph representation.
  • Analyzing residues in two-particle gluing of specific functions.
  • Exposing the twisted period nature of integral functions.
  • Applying intersection theory to derive differential equations.

Main Results:

  • A new approach is presented for analyzing specific residues in N=4 super Yang-Mills theory.
  • The twisted period nature of integral functions was identified.
  • Canonical differential equations were derived using intersection theory.
  • A solution to these equations was presented.

Conclusions:

  • The proposed method offers a pathway to overcome analytical computation challenges in N=4 super Yang-Mills theory.
  • The application of intersection theory provides a powerful tool for deriving and solving differential equations in this context.
  • This work advances the understanding and computation of higher-point functions in quantum field theory.