Cluster Adjacency for m=2 Yangian Invariants

Tomasz Lukowski; Matteo Parisi; Marcus Spradlin; Anastasia Volovich

doi:10.1007/JHEP10(2019)158

Cluster Adjacency for m=2 Yangian Invariants

Tomasz Lukowski, Matteo Parisi, Marcus Spradlin, Anastasia Volovich

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Abstract

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.

Original language	English
Article number	158
Journal	Journal of High Energy Physics (JHEP)
Volume	2019
Issue number	10
DOIs	https://doi.org/10.1007/JHEP10(2019)158
Publication status	Published - 14 Oct 2019

Keywords

hep-th
Scattering Amplitudes
Supersymmetric Gauge Theory

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10.1007/JHEP10(2019)158Licence: CC BY

Łukowski2019_Article_ClusterAdjacencyForM2YangianInFinal published version, 298 KBLicence: CC BY

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title = "Cluster Adjacency for m=2 Yangian Invariants",

abstract = " We classify the rational Yangian invariants of the \$m=2\$ toy model of \$\textbackslash{}mathcal\{N\}=4\$ Yang-Mills theory in terms of generalised triangles inside the amplituhedron \$\textbackslash{}mathcal\{A\}\_\{n,k\}\textasciicircum{}\{(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. ",

keywords = "hep-th, Scattering Amplitudes, Supersymmetric Gauge Theory",

author = "Tomasz Lukowski and Matteo Parisi and Marcus Spradlin and Anastasia Volovich",

note = "11 pages, 3 figures",

year = "2019",

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AU - Lukowski, Tomasz

AU - Parisi, Matteo

AU - Spradlin, Marcus

AU - Volovich, Anastasia

N1 - 11 pages, 3 figures

PY - 2019/10/14

Y1 - 2019/10/14

N2 - 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.

AB - 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.

KW - hep-th

KW - Scattering Amplitudes

KW - Supersymmetric Gauge Theory

UR - https://www.scopus.com/pages/publications/85073671125

U2 - 10.1007/JHEP10(2019)158

DO - 10.1007/JHEP10(2019)158

M3 - Article

SN - 1126-6708

VL - 2019

JO - Journal of High Energy Physics (JHEP)

JF - Journal of High Energy Physics (JHEP)

IS - 10

M1 - 158

ER -

Cluster Adjacency for m=2 Yangian Invariants

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