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arXiv · 1401.6446

Cluster Polylogarithms for Scattering Amplitudes

John Golden·Miguel F. Paulos·Marcus Spradlin·Anastasia Volovich
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Abstract

Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define "cluster polylogarithm functions". We find that all such functions of weight 4 are made up of a single simple building block associated to the A_2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A_2 building blocks arrange themselves to form a unique function associated to the A_3 cluster algebra. This A_3 function manifests all of the cluster algebraic structure of the two-loop n-particle MHV amplitudes for all n, and we use it to provide an explicit representation for the most complicated part of the n=7 amplitude as an example.

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John Golden, Miguel F. Paulos, Marcus Spradlin, Anastasia Volovich. 2014-07-04. Cluster Polylogarithms for Scattering Amplitudes. https://arxiv.org/abs/1401.6446

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