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arXiv · 1507.01950

Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes

Daniel E. Parker·Adam Scherlis·Marcus Spradlin·Anastasia Volovich
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Abstract

Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the $A_n$ cluster algebra. Using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.

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Daniel E. Parker, Adam Scherlis, Marcus Spradlin, Anastasia Volovich. 2015-07-07. Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes. https://doi.org/10.1007/jhep11(2015)136

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