Journal of High Energy Physics

, 2019:158 | Cite as

Cluster adjacency for m = 2 Yangian invariants

  • Tomasz ŁukowskiEmail author
  • Matteo Parisi
  • Marcus Spradlin
  • Anastasia Volovich
Open Access
Regular Article - Theoretical Physics


We classify the rational Yangian invariants of the m = 2 toy model of \( \mathcal{N} \) = 4 Yang-Mills theory in terms of generalised triangles inside the amplituhedron \( {\mathcal{A}}_{n,k}^{(2)} \). We enumerate and provide an explicit formula for all invariants for any number of particles n and any helicity degree k. Each invariant manifestly satisfies cluster adjacency with respect to the Gr(2, n) cluster algebra.


Scattering Amplitudes Supersymmetric Gauge Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Tomasz Łukowski
    • 1
    Email author
  • Matteo Parisi
    • 2
  • Marcus Spradlin
    • 3
    • 4
  • Anastasia Volovich
    • 3
  1. 1.School of Physics, Astronomy and MathematicsUniversity of HertfordshireHertfordshireU.K.
  2. 2.Mathematical InstituteUniversity of OxfordOxfordU.K.
  3. 3.Department of PhysicsBrown UniversityProvidenceU.S.A.
  4. 4.Brown Theoretical Physics CenterBrown UniversityProvidenceU.S.A.

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