Cluster algebras in scattering amplitudes with special 2D kinematics

Abstract

We study the cluster algebra of the kinematic configuration space $Con{f}_n({\mathbb{P}}^3)$ of a n-particle scattering amplitude restricted to the special 2D kinematics. We found that the n-points two loop MHV remainder function found in special 2D kinematics depend on a selection of \XX-coordinates that are part of a special structure of the cluster algebra related to snake triangulations of polygons. This structure forms a necklace of hypercubes beads in the corresponding Stasheff polytope. Furthermore in $n=12$, the cluster algebra and the selection of \XX-coordinates in special 2D kinematics replicates the cluster algebra and the selection of \XX-coordinates of $n=6$ two loop MHV amplitude in 4D kinematics.

22 pages

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Cited by in corpus (5)

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• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• Cluster Polylogarithms for Scattering Amplitudes
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras