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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AU - Parisi, Matteo

AU - Spradlin, Marcus

AU - Volovich, Anastasia

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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

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U2 - 10.1007/JHEP10(2019)158

DO - 10.1007/JHEP10(2019)158

M3 - Article

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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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Keywords

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