The University of Southampton
University of Southampton Institutional Repository
Warning ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

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
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.
1-28
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.
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, 1-28. (doi:10.1007/JHEP03(2015)072).

Record type: Article

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.

Text
__filestore.soton.ac.uk_users_skr1c15_mydocuments_eprints_Theory_Drummond_A symbol of uniqueness.pdf - Accepted Manuscript
Download (322kB)
Text
art_10.1007_JHEP03(2015)072.pdf - Version of Record
Available under License Creative Commons Attribution.
Download (591kB)

More information

Accepted/In Press date: 6 February 2015
e-pub ahead of print date: 16 March 2015
Organisations: Theoretical Partical Physics Group

Identifiers

Local EPrints ID: 402040
URI: http://eprints.soton.ac.uk/id/eprint/402040
PURE UUID: ffeaf94f-0672-490b-acdc-356970f88dac

Catalogue record

Date deposited: 27 Oct 2016 08:48
Last modified: 25 Nov 2021 21:04

Export record

Altmetrics

Contributors

Author: J.M. Drummond
Author: G. Papathanasiou
Author: M. Spradlin

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×