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Title: A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon

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 ll 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.

Authors:
 [1];  [2];  [3]
  1. University of Southampton (United Kingdom). School of Physics & Astronomy; European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division, Physics Department
  2. Université de Savoie, Annecy-le-Vieux Cedex (France). LAPTh, CNRS
  3. Brown Univ., Providence, RI (United States)
Publication Date:
Research Org.:
Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1454720
Grant/Contract Number:  
SC0010010
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2015; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Extended Supersymmetry; Scattering Amplitudes; 1/N Expansion

Citation Formats

Drummond, J. M., Papathanasiou, G., and Spradlin, M. A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon. United States: N. p., 2015. Web. doi:10.1007/JHEP03(2015)072.
Drummond, J. M., Papathanasiou, G., & Spradlin, M. A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon. United States. doi:10.1007/JHEP03(2015)072.
Drummond, J. M., Papathanasiou, G., and Spradlin, M. Mon . "A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon". United States. doi:10.1007/JHEP03(2015)072. https://www.osti.gov/servlets/purl/1454720.
@article{osti_1454720,
title = {A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon},
author = {Drummond, J. M. and Papathanasiou, G. and Spradlin, M.},
abstractNote = {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 ll 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.},
doi = {10.1007/JHEP03(2015)072},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 3,
volume = 2015,
place = {United States},
year = {2015},
month = {3}
}

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Cited by: 48 works
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    Works referencing / citing this record:

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