Cluster algebras in scattering amplitudes with special 2D kinematics

Marcus A. C. Torres

doi:10.1140/epjc/s10052-014-2757-y

EPJ

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2014) 74: 2757
https://doi.org/10.1140/epjc/s10052-014-2757-y

Regular Article - Theoretical Physics

Cluster algebras in scattering amplitudes with special 2D kinematics

Marcus A. C. Torres^*

Institut de Physique Théorique, CEA-Saclay, 91191, Gif-sur-Yvette Cedex, France

^* e-mail: marcus-andre.de-carvalho-torres@cea.fr

Received: 30 October 2013
Accepted: 27 January 2014
Published online: 27 February 2014

Abstract

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