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arXiv · 1412.3763

A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

James M. Drummond·Georgios Papathanasiou·Marcus Spradlin
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Abstract

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4,7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the $7 \parallel 6$ collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the three-loop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n>6.

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James M. Drummond, Georgios Papathanasiou, Marcus Spradlin. 2015-11-10. A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon. https://doi.org/10.1007/jhep03(2015)072

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