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Split-Helicity Tree Amplitudes and Flag Cluster Algebras

High Energy Physics - Theory 2025-12-11 v1

Abstract

Recent work has uncovered a connection between the symbol letters of general massless scattering and (permutations of) cluster variables of partial flag varieties. In this paper we explore the cluster adjacency of tree-level gluon amplitudes, specifically focusing on split-helicity amplitudes which can be written in closed form in terms of zigzag diagrams. We check in several cases, and conjecture in general, that the poles in each term satisfy cluster adjacency under a set of permutations that is built from arc permutations of the corresponding zigzag.

Keywords

Cite

@article{arxiv.2512.09704,
  title  = {Split-Helicity Tree Amplitudes and Flag Cluster Algebras},
  author = {Shruti Paranjape and Marcus Spradlin and Anastasia Volovich and He-Chen Weng},
  journal= {arXiv preprint arXiv:2512.09704},
  year   = {2025}
}

Comments

11 pages, 2 figures

R2 v1 2026-07-01T08:18:56.114Z