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Cluster Algebras for Feynman Integrals.

Dmitry Chicherin1, Johannes M Henn1, Georgios Papathanasiou2

  • 1Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München, Germany.

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Summary
This summary is machine-generated.

This study introduces cluster algebras to Feynman integrals, revealing a C2 cluster algebra structure for specific four-point integrals. This connection simplifies function spaces in particle physics calculations.

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Area of Science:

  • Theoretical Particle Physics
  • Quantum Field Theory
  • Algebraic Combinatorics

Background:

  • Feynman integrals are essential for perturbative calculations in quantum field theory.
  • Dimensional regularization is a standard technique for handling divergences.
  • Cluster algebras offer a combinatorial framework with potential applications in physics.

Purpose of the Study:

  • To explore the relationship between cluster algebras and Feynman integrals.
  • To investigate the structure of specific Feynman integrals using cluster algebra properties.
  • To identify connections between cluster algebras and known relations in scattering amplitudes.

Main Methods:

  • Initiated the study of cluster algebras within the context of Feynman integrals.
  • Analyzed four-point Feynman integrals with one off-shell leg.
  • Utilized embedding of C2 cluster algebra within A3 for identifying relations.

Main Results:

  • Provided evidence that certain four-point Feynman integrals are described by a C2 cluster algebra.
  • Identified cluster adjacency relations that constrain the allowed function space.
  • Connected these adjacencies to extended Steinmann relations for six-particle massless scattering.

Conclusions:

  • The study establishes a novel link between cluster algebras and Feynman integrals.
  • This connection offers a new perspective for restricting function spaces in amplitudes and form factors.
  • General procedures were developed for relating generalized polylogarithmic function alphabets to cluster algebras.