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arXiv · 1310.6906

Cluster algebras in scattering amplitudes with special 2D kinematics

Marcus A. C. Torres
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Abstract

We study the cluster algebra of the kinematic configuration space $Conf_n(\mathbb{P}^3)$ 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.

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Marcus A. C. Torres. 2014-01-28. Cluster algebras in scattering amplitudes with special 2D kinematics. https://doi.org/10.1140/epjc%2Fs10052-014-2757-y

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