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:
-
- University of Southampton (United Kingdom). School of Physics & Astronomy; European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division, Physics Department
- Université de Savoie, Annecy-le-Vieux Cedex (France). LAPTh, CNRS
- 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:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); 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. https://doi.org/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. https://doi.org/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)},
number = 3,
volume = 2015,
place = {United States},
year = {2015},
month = {3}
}
Web of Science
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Gluing Ladder Feynman Diagrams into Fishnets
journal, August 2017
- Basso, Benjamin; Dixon, Lance J.
- Physical Review Letters, Vol. 119, Issue 7
Cluster Adjacency Properties of Scattering Amplitudes in Supersymmetric Yang-Mills Theory
journal, April 2018
- Drummond, James; Foster, Jack; Gürdoğan, Ömer
- Physical Review Letters, Vol. 120, Issue 16
Full-Color Two-Loop Four-Gluon Amplitude in Supersymmetric QCD
journal, December 2019
- Duhr, Claude; Johansson, Henrik; Kälin, Gregor
- Physical Review Letters, Vol. 123, Issue 24
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
journal, April 2020
- Del Duca, V.; Druc, S.; Drummond, J. M.
- Physical Review Letters, Vol. 124, Issue 16
Origin of the Six-Gluon Amplitude in Planar Supersymmetric Yang-Mills Theory
journal, April 2020
- Basso, Benjamin; Dixon, Lance J.; Papathanasiou, Georgios
- Physical Review Letters, Vol. 124, Issue 16
Systematics of the multi-Regge three-loop symbol
text, January 2017
- Bargheer, Till
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
text, January 2018
- Del Duca, Vittorio; Druc, Stefan; Drummond, James
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes
journal, September 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Journal of High Energy Physics, Vol. 2019, Issue 9
Bootstrapping two-loop Feynman integrals for planar N = 4 $$ \mathcal{N}=4 $$ sYM
journal, October 2018
- Henn, Johannes; Herrmann, Enrico; Parra-Martinez, Julio
- Journal of High Energy Physics, Vol. 2018, Issue 10
The two-loop symbol of all multi-Regge regions
text, January 2016
- Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
text, January 2018
- Del Duca, Vittorio; Druc, Stefan; Drummond, James
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Cluster adjacency and the four-loop NMHV heptagon
text, January 2019
- Drummond, James; Foster, Jack; Gürdoğn, Ömer
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Systematics of the Multi-Regge Three-Loop Symbol
text, January 2016
- Bargheer, Till
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
All-order amplitudes at any multiplicity in the multi-Regge limit
text, January 2020
- Del Duca, V.; Druc, S.; Drummond, J. M.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Cluster adjacency and the four-loop NMHV heptagon
text, January 2018
- Drummond, James; Foster, Jack; Gürdoğan, Ömer
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes
text, January 2019
- Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
All-order amplitudes at any multiplicity in the multi-Regge limit
text, January 2019
- Del Duca, V.; Druc, S.; Drummond, J. M.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The double pentaladder integral to all ordersC
text, January 2018
- Caron-Huot, Simon; Dixon, Lance J.; Von Hippel, Matt
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
text, January 2020
- Del Duca, Vittorio; Druc, S.; Drummond, James M.
- ETH Zurich
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
journal, June 2018
- Del Duca, Vittorio; Druc, Stefan; Drummond, James
- Journal of High Energy Physics, Vol. 2018, Issue 6
Non-Planar On-Shell Diagrams
preprint, January 2015
- Franco, Sebastian; Galloni, Daniele; Penante, Brenda
- arXiv
The Two-Loop Symbol of all Multi-Regge Regions
text, January 2015
- Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
- arXiv
Evidence for a Nonplanar Amplituhedron
text, January 2015
- Bern, Zvi; Herrmann, Enrico; Litsey, Sean
- arXiv
Heptagons from the Steinmann Cluster Bootstrap
text, January 2016
- Dixon, Lance J.; Drummond, James; Harrington, Thomas
- arXiv
Prescriptive Unitarity
text, January 2017
- Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav
- arXiv
Quantum Gravity from Conformal Field Theory
text, January 2017
- Aprile, F.; Drummond, J. M.; Heslop, P.
- arXiv
Bootstrapping the QCD soft anomalous dimension
text, January 2017
- Almelid, Øyvind; Duhr, Claude; Gardi, Einan
- arXiv
All-Helicity Symbol Alphabets from Unwound Amplituhedra
text, January 2017
- Prlina, Igor; Spradlin, Marcus; Stankowicz, James
- arXiv
Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
text, January 2017
- Prlina, Igor; Spradlin, Marcus; Stankowicz, James
- arXiv
Rationalizing Loop Integration
text, January 2018
- Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt
- arXiv
The Double Pentaladder Integral to All Orders
text, January 2018
- Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt
- arXiv
Cluster adjacency and the four-loop NMHV heptagon
text, January 2018
- Drummond, James; Foster, Jack; Gürdoğan, Ömer
- arXiv
Elliptic polylogarithms and Feynman parameter integrals
text, January 2019
- Broedel, Johannes; Duhr, Claude; Dulat, Falko
- arXiv
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
text, January 2019
- Golden, John; McLeod, Andrew J.; Spradlin, Marcus
- arXiv
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
text, January 2019
- Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
- arXiv