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

Drummond, J. M.; Papathanasiou, G.; Spradlin, M.

doi:10.1007/JHEP03(2015)072

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:

Drummond, J. M. ^[1]; Papathanasiou, G. ^[2]; Spradlin, M. ^[3]

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:: 2015-03-16

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.

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                    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

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                    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.

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@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}

}

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DOI: 10.48550/arxiv.1306.2058

Hexagon Wilson Loop OPE and Harmonic Polylogarithms
text, January 2013

Papathanasiou, Georgios
arXiv
DOI: 10.48550/arxiv.1310.5735

The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
text, January 2014

Dixon, Lance J.; Drummond, James M.; Duhr, Claude
arXiv
DOI: 10.48550/arxiv.1402.3300

Adjoint BFKL at finite coupling: a short-cut from the collinear limit
text, January 2014

Basso, Benjamin; Caron-Huot, Simon; Sever, Amit
arXiv
DOI: 10.48550/arxiv.1407.3766

Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory
preprint, January 2014

Dixon, Lance J.; Drummond, James M.; Duhr, Claude
arXiv
DOI: 10.48550/arxiv.1407.4724

Bootstrapping an NMHV amplitude through three loops
text, January 2014

Dixon, Lance J.; von Hippel, Matt
arXiv
DOI: 10.48550/arxiv.1408.1505

One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
text, January 1994

Bern, Z.; Dixon, L.; Dunbar, D. C.
arXiv
DOI: 10.48550/arxiv.hep-ph/9403226

Cluster algebras II: Finite type classification
text, January 2002

Fomin, Sergey; Zelevinsky, Andrei
arXiv
DOI: 10.48550/arxiv.math/0208229

Cluster ensembles, quantization and the dilogarithm
preprint, January 2003

Fock, V. V.; Goncharov, A. B.
arXiv
DOI: 10.48550/arxiv.math/0311245

Works referencing / citing this record:

The four-loop six-gluon NMHV ratio function
journal, January 2016

Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.
Journal of High Energy Physics, Vol. 2016, Issue 1
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Quantum gravity from conformal field theory
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Aprile, F.; Drummond, J. M.; Heslop, P.
Journal of High Energy Physics, Vol. 2018, Issue 1
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Cluster algebras and the subalgebra constructibility of the seven-particle remainder function
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Golden, John; McLeod, Andrew J.
Journal of High Energy Physics, Vol. 2019, Issue 1
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Heptagons from the Steinmann cluster bootstrap
journal, February 2017

Dixon, Lance J.; Drummond, James; Harrington, Thomas
Journal of High Energy Physics, Vol. 2017, Issue 2
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Cluster adjacency beyond MHV
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Drummond, James; Foster, Jack; Gürdoğan, Ömer
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/jhep03(2019)086

Cluster adjacency and the four-loop NMHV heptagon
journal, March 2019

Drummond, James; Foster, Jack; Gürdoğn, Ömer
Journal of High Energy Physics, Vol. 2019, Issue 3
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The Sklyanin bracket and cluster adjacency at all multiplicity
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Golden, John; McLeod, Andrew J.; Spradlin, Marcus
Journal of High Energy Physics, Vol. 2019, Issue 3
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Boundaries of amplituhedra and NMHV symbol alphabets at two loops
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Prlina, I.; Spradlin, M.; Stankowicz, J.
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The two-loop symbol of all multi-Regge regions
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Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
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Prlina, I.; Spradlin, M.; Stankowicz, J.
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Elliptic polylogarithms and Feynman parameter integrals
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Broedel, Johannes; Duhr, Claude; Dulat, Falko
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Non-planar on-shell diagrams
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Franco, Sebastián; Galloni, Daniele; Penante, Brenda
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Evidence for a nonplanar amplituhedron
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Bern, Zvi; Herrmann, Enrico; Litsey, Sean
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Prescriptive unitarity
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Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav
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Landau singularities from the amplituhedron
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Dennen, T.; Prlina, I.; Spradlin, M.
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The double pentaladder integral to all orders
journal, July 2018

Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt
Journal of High Energy Physics, Vol. 2018, Issue 7
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Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
journal, August 2018

Broedel, Johannes; Duhr, Claude; Dulat, Falko
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Rationalizing loop integration
journal, August 2018

Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt
Journal of High Energy Physics, Vol. 2018, Issue 8
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Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops
journal, August 2019

Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko
Journal of High Energy Physics, Vol. 2019, Issue 8
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PolyLogTools — polylogs for the masses
journal, August 2019

Duhr, Claude; Dulat, Falko
Journal of High Energy Physics, Vol. 2019, Issue 8
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Bootstrapping the QCD soft anomalous dimension
journal, September 2017

Almelid, Øyvind; Duhr, Claude; Gardi, Einan
Journal of High Energy Physics, Vol. 2017, Issue 9
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Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams
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Bourjaily, Jacob L.; Franco, Sebastián; Galloni, Daniele
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Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills
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Gravity on-shell diagrams
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Herrmann, Enrico; Trnka, Jaroslav
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Prescriptive unitarity for non-planar six-particle amplitudes at two loops
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Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
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Gluing Ladder Feynman Diagrams into Fishnets
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Basso, Benjamin; Dixon, Lance J.
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Cluster Adjacency Properties of Scattering Amplitudes in $N = 4$ Supersymmetric Yang-Mills Theory
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Drummond, James; Foster, Jack; Gürdoğan, Ömer
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Full-Color Two-Loop Four-Gluon Amplitude in $N = 2$ Supersymmetric QCD
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Duhr, Claude; Johansson, Henrik; Kälin, Gregor
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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
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Origin of the Six-Gluon Amplitude in Planar $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2020

Basso, Benjamin; Dixon, Lance J.; Papathanasiou, Georgios
Physical Review Letters, Vol. 124, Issue 16
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Systematics of the multi-Regge three-loop symbol
text, January 2017

Bargheer, Till
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-12764

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
DOI: 10.3204/pubdb-2018-02259

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
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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
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Bootstrapping two-loop Feynman integrals for planar N = 4 $$ \mathcal{N}=4 $$ sYM
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Henn, Johannes; Herrmann, Enrico; Parra-Martinez, Julio
Journal of High Energy Physics, Vol. 2018, Issue 10
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The two-loop symbol of all multi-Regge regions
text, January 2016

Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
Deutsches Elektronen-Synchrotron, DESY, Hamburg
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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
DOI: 10.3204/pubdb-2018-03272

Cluster adjacency and the four-loop NMHV heptagon
text, January 2019

Drummond, James; Foster, Jack; Gürdoğn, Ömer
Deutsches Elektronen-Synchrotron, DESY, Hamburg
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Systematics of the Multi-Regge Three-Loop Symbol
text, January 2016

Bargheer, Till
Deutsches Elektronen-Synchrotron, DESY, Hamburg
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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
DOI: 10.3204/pubdb-2020-01808

Cluster adjacency and the four-loop NMHV heptagon
text, January 2018

Drummond, James; Foster, Jack; Gürdoğan, Ömer
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-05809

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
DOI: 10.3204/pubdb-2019-01783

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
DOI: 10.3204/pubdb-2019-02565

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
DOI: 10.3204/pubdb-2020-00194

The double pentaladder integral to all ordersC
text, January 2018

Caron-Huot, Simon; Dixon, Lance J.; Von Hippel, Matt
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-05437

All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
text, January 2020

Del Duca, Vittorio; Druc, S.; Drummond, James M.
ETH Zurich
DOI: 10.3929/ethz-b-000412664

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
DOI: 10.1007/jhep06(2018)116

Non-Planar On-Shell Diagrams
preprint, January 2015

Franco, Sebastian; Galloni, Daniele; Penante, Brenda
arXiv
DOI: 10.48550/arxiv.1502.02034

The Two-Loop Symbol of all Multi-Regge Regions
text, January 2015

Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
arXiv
DOI: 10.48550/arxiv.1512.07620

Evidence for a Nonplanar Amplituhedron
text, January 2015

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
arXiv
DOI: 10.48550/arxiv.1512.08591

Gravity On-shell Diagrams
text, January 2016

Herrmann, Enrico; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1604.03479

Systematics of the Multi-Regge Three-Loop Symbol
text, January 2016

Bargheer, Till
arXiv
DOI: 10.48550/arxiv.1606.07640

Heptagons from the Steinmann Cluster Bootstrap
text, January 2016

Dixon, Lance J.; Drummond, James; Harrington, Thomas
arXiv
DOI: 10.48550/arxiv.1612.08976

Prescriptive Unitarity
text, January 2017

Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1704.05460

Quantum Gravity from Conformal Field Theory
text, January 2017

Aprile, F.; Drummond, J. M.; Heslop, P.
arXiv
DOI: 10.48550/arxiv.1706.02822

Bootstrapping the QCD soft anomalous dimension
text, January 2017

Almelid, Øyvind; Duhr, Claude; Gardi, Einan
arXiv
DOI: 10.48550/arxiv.1706.10162

All-Helicity Symbol Alphabets from Unwound Amplituhedra
text, January 2017

Prlina, Igor; Spradlin, Marcus; Stankowicz, James
arXiv
DOI: 10.48550/arxiv.1711.11507

Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
text, January 2017

Prlina, Igor; Spradlin, Marcus; Stankowicz, James
arXiv
DOI: 10.48550/arxiv.1712.08049

Rationalizing Loop Integration
text, January 2018

Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt
arXiv
DOI: 10.48550/arxiv.1805.10281

The Double Pentaladder Integral to All Orders
text, January 2018

Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt
arXiv
DOI: 10.48550/arxiv.1806.01361

Cluster adjacency beyond MHV
text, January 2018

Drummond, James; Foster, Jack; Gurdogan, Omer
arXiv
DOI: 10.48550/arxiv.1810.08149

Cluster adjacency and the four-loop NMHV heptagon
text, January 2018

Drummond, James; Foster, Jack; Gürdoğan, Ömer
arXiv
DOI: 10.48550/arxiv.1812.04640

Elliptic polylogarithms and Feynman parameter integrals
text, January 2019

Broedel, Johannes; Duhr, Claude; Dulat, Falko
arXiv
DOI: 10.48550/arxiv.1902.09971

The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
text, January 2019

Golden, John; McLeod, Andrew J.; Spradlin, Marcus
arXiv
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PolyLogTools - Polylogs for the masses
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Duhr, Claude; Dulat, Falko
arXiv
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text, January 2019

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

Abstract

Citation Formats

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Notes on the scattering amplitude — Wilson loop duality journal, July 2011

A cluster bootstrap for two-loop MHV amplitudes journal, February 2015

Heptagon amplitude in the multi-Regge regime journal, October 2014

Conformal properties of four-gluon planar amplitudes and Wilson loops journal, May 2008

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N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution journal, December 2009

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On planar gluon amplitudes/Wilson loops duality journal, May 2008

MHV amplitudes in super-Yang–Mills and Wilson Loops journal, May 2008

Fast Solvers for Dense Linear Systems journal, October 2008

Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills journal, May 1997

Adjoint BFKL at finite coupling: a short-cut from the collinear limit journal, January 2015

Review of AdS/CFT Integrability: An Overview journal, October 2011

Galois symmetries of fundamental groupoids and noncommutative geometry journal, June 2005

Gaussian elimination is not optimal journal, August 1969

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes journal, August 2012

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Multichannel conformal blocks for polygon Wilson loops journal, January 2012

Gluon scattering amplitudes at strong coupling journal, June 2007

Magic identities for conformal four-point integrals journal, January 2007

Analytic results for MHV Wilson loops journal, November 2010

An analytic result for the two-loop seven-point MHV amplitude in N $$ \mathcal{N} $$ = 4 SYM journal, August 2014

Iterated path integrals journal, January 1977

Comments on gluon scattering amplitudes via AdS/CFT journal, November 2007

An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal, March 2010

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A two-loop octagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal, September 2010

Bootstrapping the three-loop hexagon journal, November 2011

Spacetime and Flux Tube S -Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory journal, August 2013

Cluster algebras II: Finite type classification journal, May 2003

Eliminating spurious poles from gauge-theoretic amplitudes journal, May 2013

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Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory journal, December 2003

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory journal, March 2010

The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space journal, December 2010

Space-time S-matrix and flux tube S-matrix II. Extracting and matching data journal, January 2014

The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal, May 2010

Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills journal, December 2011

Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory journal, May 2009

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An operator product expansion for polygonal null Wilson loops journal, April 2011

Motivic amplitudes and cluster coordinates journal, January 2014

Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory journal, August 2013

The differential of all two-loop MHV amplitudes in $ \mathcal{N}=4 $ Yang-Mills theory journal, September 2013

One-loop n-point gauge theory amplitudes, unitarity and collinear limits journal, August 1994

Amplitude for n -Gluon Scattering journal, June 1986

Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion journal, September 2014

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Cluster ensembles, quantization and the dilogarithm journal, January 2009

Heptagon amplitude in the multi-Regge regime text, January 2014

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes text, January 2012

Motivic amplitudes and cluster coordinates text, January 2014

Comments on gluon scattering amplitudes via AdS/CFT text, January 2007

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes text, January 2007

Hexagon Wilson loop = six-gluon MHV amplitude text, January 2008

N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution text, January 2008

Eliminating spurious poles from gauge-theoretic amplitudes preprint, January 2009

A simple construction of Grassmannian polylogarithms preprint, January 2009

Yangians, Grassmannians and T-duality text, January 2010

An Operator Product Expansion for Polygonal null Wilson Loops text, January 2010

The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory
journal, January 2013

Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions
journal, August 2014

Notes on the scattering amplitude — Wilson loop duality
journal, July 2011

A cluster bootstrap for two-loop MHV amplitudes
journal, February 2015

Heptagon amplitude in the multi-Regge regime
journal, October 2014

Conformal properties of four-gluon planar amplitudes and Wilson loops
journal, May 2008

Bootstrapping an NMHV amplitude through three loops
journal, October 2014

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution
journal, December 2009

Hexagon functions and the three-loop remainder function
journal, December 2013

Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory
journal, January 2012

On planar gluon amplitudes/Wilson loops duality
journal, May 2008

MHV amplitudes in super-Yang–Mills and Wilson Loops
journal, May 2008

Fast Solvers for Dense Linear Systems
journal, October 2008

Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills
journal, May 1997

Adjoint BFKL at finite coupling: a short-cut from the collinear limit
journal, January 2015

Review of AdS/CFT Integrability: An Overview
journal, October 2011

Galois symmetries of fundamental groupoids and noncommutative geometry
journal, June 2005

Gaussian elimination is not optimal
journal, August 1969

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
journal, August 2012

Bootstrapping null polygon Wilson loops
journal, March 2011

Multichannel conformal blocks for polygon Wilson loops
journal, January 2012

Gluon scattering amplitudes at strong coupling
journal, June 2007

Magic identities for conformal four-point integrals
journal, January 2007

Analytic results for MHV Wilson loops
journal, November 2010

An analytic result for the two-loop seven-point MHV amplitude in N $$ \mathcal{N} $$ = 4 SYM
journal, August 2014

Iterated path integrals
journal, January 1977

Comments on gluon scattering amplitudes via AdS/CFT
journal, November 2007

An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, March 2010

Evaluating the six-point remainder function near the collinear limit
journal, October 2014

A two-loop octagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, September 2010

Bootstrapping the three-loop hexagon
journal, November 2011

Spacetime and Flux Tube $S$ -Matrices at Finite Coupling for $N = 4$ Supersymmetric Yang-Mills Theory
journal, August 2013

Cluster algebras II: Finite type classification
journal, May 2003

Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013

Two-loop polygon Wilson loops in 𝒩 = 4 SYM
journal, May 2009

Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
journal, December 2003

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory
journal, March 2010

The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
journal, December 2010

Space-time S-matrix and flux tube S-matrix II. Extracting and matching data
journal, January 2014

The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, May 2010

Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills
journal, December 2011

Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
journal, May 2009

Supersymmetric Yang-Mills theories
journal, March 1977

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
journal, February 2010

An operator product expansion for polygonal null Wilson loops
journal, April 2011

Motivic amplitudes and cluster coordinates
journal, January 2014

Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
journal, August 2013

The differential of all two-loop MHV amplitudes in $ \mathcal{N}=4 $ Yang-Mills theory
journal, September 2013

One-loop n-point gauge theory amplitudes, unitarity and collinear limits
journal, August 1994

Amplitude for $n$ -Gluon Scattering
journal, June 1986

Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion
journal, September 2014

A current algebra for some gauge theory amplitudes
journal, November 1988

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Pulling the straps of polygons
journal, December 2011

Single-valued harmonic polylogarithms and the multi-Regge limit
journal, October 2012

A simple construction of Grassmannian polylogarithms
journal, July 2013

From polygons and symbols to polylogarithmic functions
journal, October 2012

Yangians, Grassmannians and T-duality
journal, July 2010

Hexagon Wilson loop = six-gluon MHV amplitude
journal, July 2009

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory
journal, June 2014

Hexagon Wilson loop OPE and harmonic polylogarithms
journal, November 2013

Jumpstarting the all-loop S-matrix of planar $ \mathcal{N} = {4} $ super Yang-Mills
journal, July 2012

A BLAS based C library for exact linear algebra on integer matrices
conference, January 2005

Bootstrapping six-gluon scattering in planar N=4 super-Yang-Mills theory
conference, August 2014

Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$
journal, January 2009

Cluster ensembles, quantization and the dilogarithm
journal, January 2009

Heptagon amplitude in the multi-Regge regime
text, January 2014

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
text, January 2012

Motivic amplitudes and cluster coordinates
text, January 2014

Comments on gluon scattering amplitudes via AdS/CFT
text, January 2007

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
text, January 2007

Hexagon Wilson loop = six-gluon MHV amplitude
text, January 2008

N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
text, January 2008

Eliminating spurious poles from gauge-theoretic amplitudes
preprint, January 2009

A simple construction of Grassmannian polylogarithms
preprint, January 2009

Yangians, Grassmannians and T-duality
text, January 2010

An Operator Product Expansion for Polygonal null Wilson Loops
text, January 2010

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

Analytic Results for MHV Wilson Loops
text, January 2010

Notes on the scattering amplitude / Wilson loop duality
text, January 2010