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Six-Gluon amplitudes in planar \( \mathcal{N} \) = 4 super-Yang-Mills theory at six and seven loops

  • Simon Caron-Huot
  • Lance J. Dixon
  • Falko Dulat
  • Matt von Hippel
  • Andrew J. McLeodEmail author
  • Georgios Papathanasiou
Open Access
Regular Article - Theoretical Physics

Abstract

We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.

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

  • Simon Caron-Huot
    • 1
  • Lance J. Dixon
    • 2
    • 3
    • 4
  • Falko Dulat
    • 2
  • Matt von Hippel
    • 5
    • 6
  • Andrew J. McLeod
    • 2
    • 3
    • 6
    Email author
  • Georgios Papathanasiou
    • 3
    • 7
  1. 1.Department of PhysicsMcGill UniversityMontréalCanada
  2. 2.SLAC National Accelerator LaboratoryStanford UniversityStanfordU.S.A.
  3. 3.Kavli Institute for Theoretical PhysicsUC Santa BarbaraSanta BarbaraU.S.A.
  4. 4.Institut für Physik and IRIS AdlershofHumboldt-Universität zu BerlinBerlinGermany
  5. 5.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  6. 6.Niels Bohr International AcademyCopenhagenDenmark
  7. 7.DESY Theory GroupDESY HamburgHamburgGermany

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