DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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:
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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 48 works
Citation information provided by
Web of Science

Save / Share:

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


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


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


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


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


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

  • 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


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

  • 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


Gluon scattering amplitudes at strong coupling
journal, June 2007


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


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


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

  • 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


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


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

  • 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


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

  • 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


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

  • 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


Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010


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


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


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

  • 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


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

  • 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

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


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


Review of AdS/CFT Integrability: An Overview
text, January 2010


Pulling the straps of polygons
text, January 2011


Bootstrapping the three-loop hexagon
text, January 2011


From polygons and symbols to polylogarithmic functions
text, January 2011


Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
text, January 2011


The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
text, January 2012


Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
text, January 2013


Hexagon Wilson Loop OPE and Harmonic Polylogarithms
text, January 2013


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


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


Bootstrapping an NMHV amplitude through three loops
text, January 2014


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


Cluster algebras II: Finite type classification
text, January 2002


Cluster ensembles, quantization and the dilogarithm
preprint, January 2003


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
  • 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


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

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

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

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

PolyLogTools — polylogs for the masses
journal, August 2019


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


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


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


Systematics of the multi-Regge three-loop symbol
text, January 2017


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
  • DOI: 10.3204/pubdb-2019-03749

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

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
  • DOI: 10.1007/jhep10(2018)059

The two-loop symbol of all multi-Regge regions
text, January 2016

  • Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
  • DOI: 10.3204/pubdb-2016-02009

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
  • DOI: 10.3204/pubdb-2019-01988

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


All-order amplitudes at any multiplicity in the multi-Regge limit
text, January 2020


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


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


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


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


Evidence for a Nonplanar Amplituhedron
text, January 2015


Gravity On-shell Diagrams
text, January 2016


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


Heptagons from the Steinmann Cluster Bootstrap
text, January 2016


Prescriptive Unitarity
text, January 2017


Quantum Gravity from Conformal Field Theory
text, January 2017


Bootstrapping the QCD soft anomalous dimension
text, January 2017


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


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


Rationalizing Loop Integration
text, January 2018


The Double Pentaladder Integral to All Orders
text, January 2018


Cluster adjacency beyond MHV
text, January 2018


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


Elliptic polylogarithms and Feynman parameter integrals
text, January 2019


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


PolyLogTools - Polylogs for the masses
text, January 2019


Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
text, January 2019