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Journal of High Energy Physics

, 2019:93 | Cite as

Weak separation, positivity and extremal Yangian invariants

  • Luke Lippstreu
  • Jorge Mago
  • Marcus SpradlinEmail author
  • Anastasia Volovich
Open Access
Regular Article - Theoretical Physics
  • 10 Downloads

Abstract

We classify all positive n-particle NkMHV Yangian invariants in \( \mathcal{N} \) = 4 YangMills theory with n = 5k, which we call extremal because none exist for n > 5k. We show that this problem is equivalent to that of enumerating plane cactus graphs with k pentagons. We use the known solution of that problem to provide an exact expression for the number of cyclic classes of such invariants for any k, and a simple rule for writing them down explicitly. We provide an alternative (but equivalent) classification by showing that a product of k five-brackets with disjoint sets of indices is a positive Yangian invariant if and only if the sets are all weakly separated.

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

13130_2019_11276_MOESM1_ESM.m (740 kb)
Esm 1 (M 740 kb)

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Luke Lippstreu
    • 1
  • Jorge Mago
    • 1
  • Marcus Spradlin
    • 2
    Email author
  • Anastasia Volovich
    • 1
  1. 1.Department of PhysicsBrown UniversityProvidenceU.S.A.
  2. 2.Department of Physics and Brown Theoretical Physics CenterBrown UniversityProvidenceU.S.A.

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