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Title: Weak separation, positivity and extremal Yangian invariants

Abstract

We classify all positive $n$-particle N kMHV Yangian invariants in $N =$ 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.

Authors:
 [1];  [1];  [1];  [1]
  1. Brown Univ., Providence, RI (United States)
Publication Date:
Research Org.:
Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1594824
Report Number(s):
arXiv:1906.11034
Journal ID: ISSN 1029-8479
Grant/Contract Number:  
SC0010010
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Supersymmetric Gauge Theory

Citation Formats

Lippstreu, Luke, Mago, Jorge, Spradlin, Marcus, and Volovich, Anastasia. Weak separation, positivity and extremal Yangian invariants. United States: N. p., 2019. Web. doi:10.1007/JHEP09(2019)093.
Lippstreu, Luke, Mago, Jorge, Spradlin, Marcus, & Volovich, Anastasia. Weak separation, positivity and extremal Yangian invariants. United States. doi:10.1007/JHEP09(2019)093.
Lippstreu, Luke, Mago, Jorge, Spradlin, Marcus, and Volovich, Anastasia. Thu . "Weak separation, positivity and extremal Yangian invariants". United States. doi:10.1007/JHEP09(2019)093. https://www.osti.gov/servlets/purl/1594824.
@article{osti_1594824,
title = {Weak separation, positivity and extremal Yangian invariants},
author = {Lippstreu, Luke and Mago, Jorge and Spradlin, Marcus and Volovich, Anastasia},
abstractNote = {We classify all positive $n$-particle NkMHV Yangian invariants in $N =$ 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.},
doi = {10.1007/JHEP09(2019)093},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2019,
place = {United States},
year = {2019},
month = {9}
}

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