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.

Copy to clipboard


                    Drummond, J. M., Papathanasiou, G., & Spradlin, M. A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon.  United States.  doi:https://doi.org/10.1007/JHEP03(2015)072

Copy to clipboard


                    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:https://doi.org/10.1007/JHEP03(2015)072.  https://www.osti.gov/servlets/purl/1454720.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: https://doi.org/10.1007/JHEP03(2015)072

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 48 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

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

Lipatov, Lev; Prygarin, Alexander; Schnitzer, Howard J.
Journal of High Energy Physics, Vol. 2013, Issue 1
DOI: 10.1007/JHEP01(2013)068

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

Basso, Benjamin; Sever, Amit; Vieira, Pedro
Journal of High Energy Physics, Vol. 2014, Issue 8
DOI: 10.1007/JHEP08(2014)085

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

Caron-Huot, S.
Journal of High Energy Physics, Vol. 2011, Issue 7
DOI: 10.1007/JHEP07(2011)058

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

Golden, John; Spradlin, Marcus
Journal of High Energy Physics, Vol. 2015, Issue 2
DOI: 10.1007/JHEP02(2015)002

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

Bartels, J.; Schomerus, V.; Sprenger, M.
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)067

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

Drummond, J. M.; Korchemsky, G. P.; Sokatchev, E.
Nuclear Physics B, Vol. 795, Issue 1-2
DOI: 10.1016/j.nuclphysb.2007.11.041

Bootstrapping an NMHV amplitude through three loops
journal, October 2014

Dixon, Lance J.; von Hippel, Matt
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)065

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

Bartels, J.; Lipatov, L. N.; Sabio Vera, A.
The European Physical Journal C, Vol. 65, Issue 3-4
DOI: 10.1140/epjc/s10052-009-1218-5

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

Dixon, Lance J.; Drummond, James M.; von Hippel, Matt
Journal of High Energy Physics, Vol. 2013, Issue 12
DOI: 10.1007/JHEP12(2013)049

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

Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
Journal of High Energy Physics, Vol. 2012, Issue 1
DOI: 10.1007/JHEP01(2012)024

MHV amplitude for <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mn>3</mml:mn><mml:mo>→</mml:mo><mml:mn>3</mml:mn></mml:math> gluon scattering in Regge limit
journal, November 2011

Bartels, J.; Lipatov, L. N.; Prygarin, A.
Physics Letters B, Vol. 705, Issue 5
DOI: 10.1016/j.physletb.2011.09.061

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

Drummond, J. M.; Henn, J.; Korchemsky, G. P.
Nuclear Physics B, Vol. 795, Issue 1-2
DOI: 10.1016/j.nuclphysb.2007.11.007

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

Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele
Nuclear Physics B, Vol. 794, Issue 1-2
DOI: 10.1016/j.nuclphysb.2007.11.002

Fast Solvers for Dense Linear Systems
journal, October 2008

Kauers, Manuel
Nuclear Physics B - Proceedings Supplements, Vol. 183
DOI: 10.1016/j.nuclphysbps.2008.09.111

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

Bern, Z.; Rozowsky, J. S.; Yan, B.
Physics Letters B, Vol. 401, Issue 3-4
DOI: 10.1016/S0370-2693(97)00413-9

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

Basso, Benjamin; Caron-Huot, Simon; Sever, Amit
Journal of High Energy Physics, Vol. 2015, Issue 1
DOI: 10.1007/JHEP01(2015)027

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

Beisert, Niklas; Ahn, Changrim; Alday, Luis F.
Letters in Mathematical Physics, Vol. 99, Issue 1-3
DOI: 10.1007/s11005-011-0529-2

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

Goncharov, A. B.
Duke Mathematical Journal, Vol. 128, Issue 2
DOI: 10.1215/S0012-7094-04-12822-2

Gaussian elimination is not optimal
journal, August 1969

Strassen, Volker
Numerische Mathematik, Vol. 13, Issue 4
DOI: 10.1007/BF02165411

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

Duhr, Claude
Journal of High Energy Physics, Vol. 2012, Issue 8
DOI: 10.1007/JHEP08(2012)043

Bootstrapping null polygon Wilson loops
journal, March 2011

Gaiotto, Davide; Maldacena, Juan; Sever, Amit
Journal of High Energy Physics, Vol. 2011, Issue 3
DOI: 10.1007/JHEP03(2011)092

Multichannel conformal blocks for polygon Wilson loops
journal, January 2012

Sever, Amit; Vieira, Pedro
Journal of High Energy Physics, Vol. 2012, Issue 1
DOI: 10.1007/JHEP01(2012)070

Gluon scattering amplitudes at strong coupling
journal, June 2007

Alday, Luis F.; Maldacena, Juan
Journal of High Energy Physics, Vol. 2007, Issue 06
DOI: 10.1088/1126-6708/2007/06/064

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

Drummond, James M.; Henn, Johannes; Smirnov, Vladimir A.
Journal of High Energy Physics, Vol. 2007, Issue 01
DOI: 10.1088/1126-6708/2007/01/064

Analytic results for MHV Wilson loops
journal, November 2010

Heslop, Paul; Khoze, Valentin V.
Journal of High Energy Physics, Vol. 2010, Issue 11
DOI: 10.1007/JHEP11(2010)035

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

Golden, John; Spradlin, Marcus
Journal of High Energy Physics, Vol. 2014, Issue 8
DOI: 10.1007/JHEP08(2014)154

BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> SUSY
journal, January 2012

Fadin, V. S.; Lipatov, L. N.
Physics Letters B, Vol. 706, Issue 4-5
DOI: 10.1016/j.physletb.2011.11.048

Iterated path integrals
journal, January 1977

Chen, Kuo-Tsai
Bulletin of the American Mathematical Society, Vol. 83, Issue 5
DOI: 10.1090/S0002-9904-1977-14320-6

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

Alday, Luis F.; Maldacena, Juan
Journal of High Energy Physics, Vol. 2007, Issue 11
DOI: 10.1088/1126-6708/2007/11/068

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

Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.
Journal of High Energy Physics, Vol. 2010, Issue 3
DOI: 10.1007/JHEP03(2010)099

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

Papathanasiou, Georgios
International Journal of Modern Physics A, Vol. 29, Issue 27
DOI: 10.1142/S0217751X14501541

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

Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.
Journal of High Energy Physics, Vol. 2010, Issue 9
DOI: 10.1007/JHEP09(2010)015

Bootstrapping the three-loop hexagon
journal, November 2011

Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
Journal of High Energy Physics, Vol. 2011, Issue 11
DOI: 10.1007/JHEP11(2011)023

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

Basso, Benjamin; Sever, Amit; Vieira, Pedro
Physical Review Letters, Vol. 111, Issue 9
DOI: 10.1103/PhysRevLett.111.091602

Cluster algebras II: Finite type classification
journal, May 2003

Fomin, Sergey; Zelevinsky, Andrei
Inventiones mathematicae, Vol. 154, Issue 1
DOI: 10.1007/s00222-003-0302-y

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

Hodges, Andrew
Journal of High Energy Physics, Vol. 2013, Issue 5
DOI: 10.1007/JHEP05(2013)135

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

Anastasiou, C.; Brandhuber, A.; Heslop, P.
Journal of High Energy Physics, Vol. 2009, Issue 05
DOI: 10.1088/1126-6708/2009/05/115

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

Anastasiou, C.; Dixon, L.; Bern, Z.
Physical Review Letters, Vol. 91, Issue 25
DOI: 10.1103/PhysRevLett.91.251602

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

Drummond, J. M.; Henn, J.; Korchemsky, G. P.
Nuclear Physics B, Vol. 828, Issue 1-2
DOI: 10.1016/j.nuclphysb.2009.11.022

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

Mason, Lionel; Skinner, David
Journal of High Energy Physics, Vol. 2010, Issue 12
DOI: 10.1007/JHEP12(2010)018

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

Basso, Benjamin; Sever, Amit; Vieira, Pedro
Journal of High Energy Physics, Vol. 2014, Issue 1
DOI: 10.1007/JHEP01(2014)008

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

Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.
Journal of High Energy Physics, Vol. 2010, Issue 5
DOI: 10.1007/JHEP05(2010)084

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

Caron-Huot, S.
Journal of High Energy Physics, Vol. 2011, Issue 12
DOI: 10.1007/JHEP12(2011)066

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

Drummond, James; Henn, Johannes; Plefka, Jan
Journal of High Energy Physics, Vol. 2009, Issue 05
DOI: 10.1088/1126-6708/2009/05/046

Supersymmetric Yang-Mills theories
journal, March 1977

Brink, Lars; Schwarz, John H.; Scherk, J.
Nuclear Physics B, Vol. 121, Issue 1
DOI: 10.1016/0550-3213(77)90328-5

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

Drummond, J. M.; Henn, J.; Korchemsky, G. P.
Nuclear Physics B, Vol. 826, Issue 1-2
DOI: 10.1016/j.nuclphysb.2009.10.013

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

Alday, Luis F.; Gaiotto, Davide; Maldacena, Juan
Journal of High Energy Physics, Vol. 2011, Issue 4
DOI: 10.1007/JHEP04(2011)088

Motivic amplitudes and cluster coordinates
journal, January 2014

Golden, J. K.; Goncharov, A. B.; Spradlin, M.
Journal of High Energy Physics, Vol. 2014, Issue 1
DOI: 10.1007/JHEP01(2014)091

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

Caron-Huot, Simon; He, Song
Journal of High Energy Physics, Vol. 2013, Issue 8
DOI: 10.1007/JHEP08(2013)101

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

Golden, John; Spradlin, Marcus
Journal of High Energy Physics, Vol. 2013, Issue 9
DOI: 10.1007/JHEP09(2013)111

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

Bern, Zvi; Dixon, Lance; Dunbar, David C.
Nuclear Physics B, Vol. 425, Issue 1-2
DOI: 10.1016/0550-3213(94)90179-1

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

Parke, Stephen J.; Taylor, T. R.
Physical Review Letters, Vol. 56, Issue 23
DOI: 10.1103/PhysRevLett.56.2459

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

Basso, Benjamin; Sever, Amit; Vieira, Pedro
Journal of High Energy Physics, Vol. 2014, Issue 9
DOI: 10.1007/JHEP09(2014)149

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

Nair, V. P.
Physics Letters B, Vol. 214, Issue 2
DOI: 10.1016/0370-2693(88)91471-2

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Goncharov, A. B.; Spradlin, M.; Vergu, C.
Physical Review Letters, Vol. 105, Issue 15
DOI: 10.1103/PhysRevLett.105.151605

Pulling the straps of polygons
journal, December 2011

Gaiotto, Davide; Maldacena, Juan; Sever, Amit
Journal of High Energy Physics, Vol. 2011, Issue 12
DOI: 10.1007/JHEP12(2011)011

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

Dixon, Lance J.; Duhr, Claude; Pennington, Jeffrey
Journal of High Energy Physics, Vol. 2012, Issue 10
DOI: 10.1007/JHEP10(2012)074

A simple construction of Grassmannian polylogarithms
journal, July 2013

Goncharov, A. B.
Advances in Mathematics, Vol. 241
DOI: 10.1016/j.aim.2013.03.018

From polygons and symbols to polylogarithmic functions
journal, October 2012

Duhr, Claude; Gangl, Herbert; Rhodes, John R.
Journal of High Energy Physics, Vol. 2012, Issue 10
DOI: 10.1007/JHEP10(2012)075

Yangians, Grassmannians and T-duality
journal, July 2010

Drummond, J. M.; Ferro, L.
Journal of High Energy Physics, Vol. 2010, Issue 7
DOI: 10.1007/JHEP07(2010)027

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

Drummond, J. M.; Henn, J.; Korchemsky, G. P.
Nuclear Physics B, Vol. 815, Issue 1-2
DOI: 10.1016/j.nuclphysb.2009.02.015

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

Dixon, Lance J.; Drummond, James M.; Duhr, Claude
Journal of High Energy Physics, Vol. 2014, Issue 6
DOI: 10.1007/JHEP06(2014)116

Hexagon Wilson loop OPE and harmonic polylogarithms
journal, November 2013

Papathanasiou, Georgios
Journal of High Energy Physics, Vol. 2013, Issue 11
DOI: 10.1007/JHEP11(2013)150

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

Caron-Huot, S.; He, Song
Journal of High Energy Physics, Vol. 2012, Issue 7
DOI: 10.1007/JHEP07(2012)174

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

Chen, Zhuliang; Storjohann, Arne
Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05
DOI: 10.1145/1073884.1073899

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

Dixon, Lance; Drummond, James; Duhr, Claude
Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2014)
DOI: 10.22323/1.211.0077

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

Brown, Francis C. S.
Annales scientifiques de l'École normale supérieure, Vol. 42, Issue 3
DOI: 10.24033/asens.2099

Cluster ensembles, quantization and the dilogarithm
journal, January 2009

Fock, Vladimir V.; Goncharov, Alexander B.
Annales scientifiques de l'École normale supérieure, Vol. 42, Issue 6
DOI: 10.24033/asens.2112

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

Bartels, J.; Schomerus, V.; Sprenger, M.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2014-04099

Works referencing / citing this record:

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
DOI: 10.1007/jhep08(2019)016

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
DOI: 10.1007/jhep03(2019)087

Cluster Adjacency Properties of Scattering Amplitudes in $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2018

Drummond, James; Foster, Jack; Gürdoğan, Ömer
Physical Review Letters, Vol. 120, Issue 16
DOI: 10.1103/physrevlett.120.161601

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
DOI: 10.1007/jhep09(2019)061

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
DOI: 10.1007/jhep03(2019)087

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
DOI: 10.1007/jhep08(2019)016

Cluster Adjacency Properties of Scattering Amplitudes in $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2018

Drummond, James; Foster, Jack; Gürdoğan, Ömer
Physical Review Letters, Vol. 120, Issue 16
DOI: 10.1103/physrevlett.120.161601

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
DOI: 10.3204/pubdb-2019-03749

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
DOI: 10.1103/physrevlett.124.161602

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
DOI: 10.1103/physrevlett.124.161603

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

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
DOI: 10.1007/jhep01(2016)053

Quantum gravity from conformal field theory
journal, January 2018

Aprile, F.; Drummond, J. M.; Heslop, P.
Journal of High Energy Physics, Vol. 2018, Issue 1
DOI: 10.1007/jhep01(2018)035

Cluster algebras and the subalgebra constructibility of the seven-particle remainder function
journal, January 2019

Golden, John; McLeod, Andrew J.
Journal of High Energy Physics, Vol. 2019, Issue 1
DOI: 10.1007/jhep01(2019)017

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
DOI: 10.1007/jhep02(2017)137

Cluster adjacency beyond MHV
journal, March 2019

Drummond, James; Foster, Jack; Gürdoğan, Ömer
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/jhep03(2019)086

The Sklyanin bracket and cluster adjacency at all multiplicity
journal, March 2019

Golden, John; McLeod, Andrew J.; Spradlin, Marcus
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/jhep03(2019)195

Boundaries of amplituhedra and NMHV symbol alphabets at two loops
journal, April 2018

Prlina, I.; Spradlin, M.; Stankowicz, J.
Journal of High Energy Physics, Vol. 2018, Issue 4
DOI: 10.1007/jhep04(2018)049

The two-loop symbol of all multi-Regge regions
journal, May 2016

Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
Journal of High Energy Physics, Vol. 2016, Issue 5
DOI: 10.1007/jhep05(2016)012

All-helicity symbol alphabets from unwound amplituhedra
journal, May 2018

Prlina, I.; Spradlin, M.; Stankowicz, J.
Journal of High Energy Physics, Vol. 2018, Issue 5
DOI: 10.1007/jhep05(2018)159

Bootstrapping pentagon functions
journal, May 2018

Chicherin, Dmitry; Henn, Johannes; Mitev, Vladimir
Journal of High Energy Physics, Vol. 2018, Issue 5
DOI: 10.1007/jhep05(2018)164

Elliptic polylogarithms and Feynman parameter integrals
journal, May 2019

Broedel, Johannes; Duhr, Claude; Dulat, Falko
Journal of High Energy Physics, Vol. 2019, Issue 5
DOI: 10.1007/jhep05(2019)120

Non-planar on-shell diagrams
journal, June 2015

Franco, Sebastián; Galloni, Daniele; Penante, Brenda
Journal of High Energy Physics, Vol. 2015, Issue 6
DOI: 10.1007/jhep06(2015)199

Evidence for a nonplanar amplituhedron
journal, June 2016

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
Journal of High Energy Physics, Vol. 2016, Issue 6
DOI: 10.1007/jhep06(2016)098

Prescriptive unitarity
journal, June 2017

Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2017, Issue 6
DOI: 10.1007/jhep06(2017)059

Landau singularities from the amplituhedron
journal, June 2017

Dennen, T.; Prlina, I.; Spradlin, M.
Journal of High Energy Physics, Vol. 2017, Issue 6
DOI: 10.1007/jhep06(2017)152

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
DOI: 10.1007/jhep07(2018)170

Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
journal, August 2018

Broedel, Johannes; Duhr, Claude; Dulat, Falko
Journal of High Energy Physics, Vol. 2018, Issue 8
DOI: 10.1007/jhep08(2018)014

Rationalizing loop integration
journal, August 2018

Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt
Journal of High Energy Physics, Vol. 2018, Issue 8
DOI: 10.1007/jhep08(2018)184

PolyLogTools — polylogs for the masses
journal, August 2019

Duhr, Claude; Dulat, Falko
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/jhep08(2019)135

Bootstrapping the QCD soft anomalous dimension
journal, September 2017

Almelid, Øyvind; Duhr, Claude; Gardi, Einan
Journal of High Energy Physics, Vol. 2017, Issue 9
DOI: 10.1007/jhep09(2017)073

Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams
journal, October 2016

Bourjaily, Jacob L.; Franco, Sebastián; Galloni, Daniele
Journal of High Energy Physics, Vol. 2016, Issue 10
DOI: 10.1007/jhep10(2016)003

Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills
journal, October 2019

Mago, Jorge; Schreiber, Anders; Spradlin, Marcus
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)099

Gravity on-shell diagrams
journal, November 2016

Herrmann, Enrico; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2016, Issue 11
DOI: 10.1007/jhep11(2016)136

Prescriptive unitarity for non-planar six-particle amplitudes at two loops
journal, December 2019

Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/jhep12(2019)073

Gluing Ladder Feynman Diagrams into Fishnets
journal, August 2017

Basso, Benjamin; Dixon, Lance J.
Physical Review Letters, Vol. 119, Issue 7
DOI: 10.1103/physrevlett.119.071601

Full-Color Two-Loop Four-Gluon Amplitude in $N = 2$ Supersymmetric QCD
journal, December 2019

Duhr, Claude; Johansson, Henrik; Kälin, Gregor
Physical Review Letters, Vol. 123, Issue 24
DOI: 10.1103/physrevlett.123.241601

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

Similar Records in DOE PAGES and OSTI.GOV collections:

Heptagons from the Steinmann cluster bootstrap

Journal Article Dixon, Lance J. ; Drummond, James ; Harrington, Thomas ; ... - Journal of High Energy Physics (Online)

We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planarmore »« less
Cited by 5
DOI: https://doi.org/10.1007/JHEP02(2017)137

Full Text Available
Lifting heptagon symbols to functions

Journal Article Dixon, Lance J. ; Liu, Yu-Ting - Journal of High Energy Physics (Online)

Seven-point amplitudes in planarmore »« less
DOI: https://doi.org/10.1007/jhep10(2020)031

Full Text Available
A cluster bootstrap for two-loop MHV amplitudes

Journal Article Golden, John ; Spradlin, Marcus - Journal of High Energy Physics (Online)

We apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory. We argue that the mathematically most complicated part (the Λ² B₂ coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits). Finally, we present a concise, closed-form expression which manifests these properties for all n.
Cited by 18
DOI: https://doi.org/10.1007/JHEP02(2015)002

Full Text Available
Bootstrapping the Three-Loop Hexagon

Journal Article Dixon, Lance J ; /CERN /SLAC ; Drummond, James M ; ... - JHEP 1111:023,2011

We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both ourmore »« less
DOI: https://doi.org/10.1007/JHEP11(2011)023

Full Text Available
Cluster functions and scattering amplitudes for six and seven points

Journal Article Harrington, Thomas ; Spradlin, Marcus - Journal of High Energy Physics (Online)

Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. Here, we explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4, 6) and Gr(4, 7) cluster polylogarithm functions of [15] at weight 4.
Cited by 4
DOI: https://doi.org/10.1007/JHEP07(2017)016

Full Text Available

Similar Records

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

Abstract

Citation Formats

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

Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops journal, August 2019

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

Cluster Adjacency Properties of Scattering Amplitudes in N = 4 Supersymmetric Yang-Mills Theory journal, April 2018

The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes journal, September 2019

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

Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops journal, August 2019

Cluster Adjacency Properties of Scattering Amplitudes in N = 4 Supersymmetric Yang-Mills Theory journal, April 2018

The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes text, January 2019

All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit journal, April 2020

Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory journal, April 2020

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

Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops
journal, August 2019

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

Cluster Adjacency Properties of Scattering Amplitudes in $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2018

The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes
journal, September 2019

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

Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops
journal, August 2019

Cluster Adjacency Properties of Scattering Amplitudes in $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2018

The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes
text, January 2019

All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
journal, April 2020

Origin of the Six-Gluon Amplitude in Planar $N = 4$ Supersymmetric Yang-Mills Theory
journal, April 2020

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

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

Quantum gravity from conformal field theory
journal, January 2018