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The Sklyanin bracket and cluster adjacency at all multiplicity

  • John Golden
  • Andrew J. McLeodEmail author
  • Marcus Spradlin
  • Anastasia Volovich
Open Access
Regular Article - Theoretical Physics
  • 29 Downloads

Abstract

We argue that the Sklyanin Poisson bracket on Gr(4, n) can be used to efficiently test whether an amplitude in planar \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory satisfies cluster adjacency. We use this test to show that cluster adjacency is satisfied by all one- and two-loop MHV amplitudes in this theory, once suitably regulated. Using this technique we also demonstrate that cluster adjacency implies the extended Steinmann relations at all particle multiplicities.

Keywords

Scattering Amplitudes Supersymmetric Gauge Theory 

Notes

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.

Supplementary material

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • John Golden
    • 1
  • Andrew J. McLeod
    • 2
    Email author
  • Marcus Spradlin
    • 3
  • Anastasia Volovich
    • 4
  1. 1.Leinweber Center for Theoretical Physics and Randall Laboratory of Physics, Department of PhysicsUniversity of MichiganAnn ArborU.S.A.
  2. 2.Niels Bohr International AcademyCopenhagenDenmark
  3. 3.Department of Physics and Brown Theoretical Physics CenterBrown UniversityProvidenceU.S.A.
  4. 4.Department of PhysicsBrown UniversityProvidenceU.S.A.

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