A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
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 ? 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 threeloop 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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Drummond, J.M.
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Papathanasiou, G.
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Spradlin, M.
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Drummond, J.M.
3ea15544-457f-4e72-8ad0-60f3136841db
Papathanasiou, G.
bc9d1435-82d4-4f4c-ab79-5506974a194e
Spradlin, M.
fc63aa91-9138-4659-917d-83a9bbbbc18e
Drummond, J.M., Papathanasiou, G. and Spradlin, M.
(2015)
A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon.
Journal of High Energy Physics, 72, .
(doi:10.1007/JHEP03(2015)072).
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 ? 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 threeloop 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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Accepted/In Press date: 6 February 2015
e-pub ahead of print date: 16 March 2015
Organisations:
Theoretical Partical Physics Group
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Local EPrints ID: 402040
URI: http://eprints.soton.ac.uk/id/eprint/402040
PURE UUID: ffeaf94f-0672-490b-acdc-356970f88dac
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Date deposited: 27 Oct 2016 08:48
Last modified: 15 Mar 2024 03:04
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Author:
G. Papathanasiou
Author:
M. Spradlin
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