The double pentaladder integral to all orders

Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.; Papathanasiou, Georgios

doi:10.1007/jhep07(2018)170

Title: The double pentaladder integral to all orders

Abstract

We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N = 4 super-Yang-Mills theory. We provide exact, finite-coupling formulas for the basic double pentaladder integrals as a single Mellin integral over hypergeometric functions. For particular choices of the dual conformal cross ratios, we can evaluate the integral at weak coupling to high loop orders in terms of multiple polylogarithms. We argue that the integrals are exponentially suppressed at strong coupling. Here in this paper, we describe the space of functions that contains all such double pentaladder integrals and their derivatives, or coproducts. This space, a prototype for the space of Steinmann hexagon functions, has a simple algebraic structure, which we elucidate by considering a particular discontinuity of the functions that localizes the Mellin integral and collapses the relevant symbol alphabet. This function space is endowed with a coaction, both perturbatively and at finite coupling, which mixes the independent solutions of the hypergeometric differential equation and constructively realizes a coaction principle of the type believed to hold in the full Steinmann hexagon function space.

Authors:

Caron-Huot, Simon ^[1];

^[2]; von Hippel, Matt ^[3]; McLeod, Andrew J. ^[4]; Papathanasiou, Georgios ^[5]

McGill Univ., Montreal, QC (Canada). Dept of Physics
SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Ecole Normale Superieure, Paris (France). Lab. de Physique Theorique
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Niels Bohr International Academy, Copenhagen (Denmark)
SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Niels Bohr International Academy, Copenhagen (Denmark)
Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

Publication Date:: Fri Jul 27 00:00:00 EDT 2018

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1468694

Report Number(s):: SLAC-PUB-17228
Journal ID: ISSN 1029-8479; PII: 8707

Grant/Contract Number:: AC02-76SF00515

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: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Scattering Amplitudes; Nonperturbative Effects; 1/N Expansion; Conformal and W Symmetry

Citation Formats


                    Caron-Huot, Simon, Dixon, Lance J., von Hippel, Matt, McLeod, Andrew J., and Papathanasiou, Georgios. The double pentaladder integral to all orders.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep07(2018)170.

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                    Caron-Huot, Simon, Dixon, Lance J., von Hippel, Matt, McLeod, Andrew J., & Papathanasiou, Georgios. The double pentaladder integral to all orders.  United States.  https://doi.org/10.1007/jhep07(2018)170

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                    Caron-Huot, Simon, Dixon, Lance J., von Hippel, Matt, McLeod, Andrew J., and Papathanasiou, Georgios. Fri .  
"The double pentaladder integral to all orders".  United States.  https://doi.org/10.1007/jhep07(2018)170.  https://www.osti.gov/servlets/purl/1468694.

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@article{osti_1468694,

  title        = {The double pentaladder integral to all orders},

  author       = {Caron-Huot, Simon and Dixon, Lance J. and von Hippel, Matt and McLeod, Andrew J. and Papathanasiou, Georgios},

  abstractNote = {We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N = 4 super-Yang-Mills theory. We provide exact, finite-coupling formulas for the basic double pentaladder integrals as a single Mellin integral over hypergeometric functions. For particular choices of the dual conformal cross ratios, we can evaluate the integral at weak coupling to high loop orders in terms of multiple polylogarithms. We argue that the integrals are exponentially suppressed at strong coupling. Here in this paper, we describe the space of functions that contains all such double pentaladder integrals and their derivatives, or coproducts. This space, a prototype for the space of Steinmann hexagon functions, has a simple algebraic structure, which we elucidate by considering a particular discontinuity of the functions that localizes the Mellin integral and collapses the relevant symbol alphabet. This function space is endowed with a coaction, both perturbatively and at finite coupling, which mixes the independent solutions of the hypergeometric differential equation and constructively realizes a coaction principle of the type believed to hold in the full Steinmann hexagon function space.},

  doi          = {10.1007/jhep07(2018)170},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 7,

  volume       = 2018,

  place        = {United States},

  year         = {Fri Jul 27 00:00:00 EDT 2018},

  month        = {Fri Jul 27 00:00:00 EDT 2018}

}

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Figure 1: The eight- or higher-point $L$-loop ladder integral, labelled by dual coordinates.

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Duhr, Claude
2014 Theoretical Advanced Study Institute in Elementary Particle Physics, Journeys Through the Precision Frontier: Amplitudes for Colliders
DOI: 10.1142/9789814678766_0010

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

Duhr, Claude
ETH Zurich
DOI: 10.3929/ethz-b-000058776

Motivic amplitudes and cluster coordinates
text, January 2014

Golden, J. K.; Goncharov, Alexander B.; Spradlin, Marcus
ETH Zurich
DOI: 10.3929/ethz-b-000080905

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

Hodges, Andrew
arXiv
DOI: 10.48550/arxiv.0905.1473

Dual Superconformal Invariance, Momentum Twistors and Grassmannians
text, January 2009

Mason, Lionel; Skinner, David
arXiv
DOI: 10.48550/arxiv.0909.0250

Local Spacetime Physics from the Grassmannian
text, January 2009

Arkani-Hamed, Nima; Bourjaily, Jacob; Cachazo, Freddy
arXiv
DOI: 10.48550/arxiv.0912.3249

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

Goncharov, Alexander B.; Spradlin, Marcus; Vergu, C.
arXiv
DOI: 10.48550/arxiv.1006.5703

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

Beisert, Niklas; Ahn, Changrim; Alday, Luis F.
arXiv
DOI: 10.48550/arxiv.1012.3982

Pulling the straps of polygons
text, January 2011

Gaiotto, Davide; Maldacena, Juan; Sever, Amit
arXiv
DOI: 10.48550/arxiv.1102.0062

The massless hexagon integral in D = 6 dimensions
text, January 2011

Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.
arXiv
DOI: 10.48550/arxiv.1104.2781

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
text, January 2011

Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
arXiv
DOI: 10.48550/arxiv.1104.2787

Bootstrapping the three-loop hexagon
text, January 2011

Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
arXiv
DOI: 10.48550/arxiv.1108.4461

From polygons and symbols to polylogarithmic functions
text, January 2011

Duhr, Claude; Gangl, Herbert; Rhodes, John R.
arXiv
DOI: 10.48550/arxiv.1110.0458

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

Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.
arXiv
DOI: 10.48550/arxiv.1111.1704

Hepta-Cuts of Two-Loop Scattering Amplitudes
text, January 2012

Badger, Simon; Frellesvig, Hjalte; Zhang, Yang
arXiv
DOI: 10.48550/arxiv.1202.2019

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

Duhr, Claude
arXiv
DOI: 10.48550/arxiv.1203.0454

Mellin Amplitudes for Dual Conformal Integrals
text, January 2012

Paulos, Miguel F.; Spradlin, Marcus; Volovich, Anastasia
arXiv
DOI: 10.48550/arxiv.1203.6362

Uniqueness of two-loop master contours
text, January 2012

Caron-Huot, Simon; Larsen, Kasper J.
arXiv
DOI: 10.48550/arxiv.1205.0801

Superstring amplitudes and the associator
text, January 2013

Drummond, J. M.; Ragoucy, E.
arXiv
DOI: 10.48550/arxiv.1301.0794

Graphical functions and single-valued multiple polylogarithms
preprint, January 2013

Schnetz, Oliver
arXiv
DOI: 10.48550/arxiv.1302.6445

Leading singularities and off-shell conformal integrals
text, January 2013

Drummond, James; Duhr, Claude; Eden, Burkhard
arXiv
DOI: 10.48550/arxiv.1303.6909

Hexagon Wilson Loop OPE and Harmonic Polylogarithms
text, January 2013

Papathanasiou, Georgios
arXiv
DOI: 10.48550/arxiv.1310.5735

Real-Virtual contributions to the inclusive Higgs cross-section at N3LO
text, January 2013

Anastasiou, Charalampos; Duhr, Claude; Dulat, Falko
arXiv
DOI: 10.48550/arxiv.1311.1425

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

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

OPE for all Helicity Amplitudes
text, January 2014

Basso, Benjamin; Caetano, Joao; Cordova, Lucia
arXiv
DOI: 10.48550/arxiv.1412.1132

Logarithmic Singularities and Maximally Supersymmetric Amplitudes
preprint, January 2014

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
arXiv
DOI: 10.48550/arxiv.1412.8584

A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
text, January 2015

Badger, Simon; Mogull, Gustav; Ochirov, Alexander
arXiv
DOI: 10.48550/arxiv.1507.08797

Evidence for a Nonplanar Amplituhedron
text, January 2015

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

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
text, January 2016

Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew
arXiv
DOI: 10.48550/arxiv.1609.00669

Hexagonalization of Correlation Functions
text, January 2016

Fleury, Thiago; Komatsu, Shota
arXiv
DOI: 10.48550/arxiv.1611.05577

Heptagons from the Steinmann Cluster Bootstrap
text, January 2016

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

The algebraic structure of cut Feynman integrals and the diagrammatic coaction
text, January 2017

Abreu, Samuel; Britto, Ruth; Duhr, Claude
arXiv
DOI: 10.48550/arxiv.1703.05064

A first look at two-loop five-gluon scattering in QCD
text, January 2017

Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu
arXiv
DOI: 10.48550/arxiv.1712.02229

Harmonic Polylogarithms
text, January 1999

Remiddi, E.; Vermaseren, J. A. M.
arXiv
DOI: 10.48550/arxiv.hep-ph/9905237

Multi-loop Feynman integrals and conformal quantum mechanics
text, January 2003

Isaev, A. P.
arXiv
DOI: 10.48550/arxiv.hep-th/0303056

On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
text, January 1998

Bern, Z.; Dixon, L.; Dunbar, D. C.
arXiv
DOI: 10.48550/arxiv.hep-th/9802162

A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
journal, October 2015

Badger, Simon; Mogull, Gustav; Ochirov, Alexander
Journal of High Energy Physics, Vol. 2015, Issue 10
DOI: 10.1007/jhep10(2015)064

Azurite : An algebraic geometry based package for finding bases of loop integrals
journal, December 2017

Georgoudis, Alessandro; Larsen, Kasper J.; Zhang, Yang
Computer Physics Communications, Vol. 221
DOI: 10.1016/j.cpc.2017.08.013

The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
text, January 2008

Bern, Z.; Dixon, L. J.; Kosower, D. A.
arXiv
DOI: 10.48550/arxiv.0803.1465

Towards a Basis for Planar Two-Loop Integrals
text, January 2010

Gluza, Janusz; Kajda, Krzysztof; Kosower, David A.
arXiv
DOI: 10.48550/arxiv.1009.0472

Two-Loop Maximal Unitarity with External Masses
text, January 2012

Johansson, Henrik; Kosower, David A.; Larsen, Kasper J.
arXiv
DOI: 10.48550/arxiv.1208.1754

Subleading Poles in the Numerical Unitarity Method at Two Loops
text, January 2017

Abreu, S.; Cordero, F. Febres; Ita, H.
arXiv
DOI: 10.48550/arxiv.1703.05255

On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
text, January 1998

Bern, Z.; Dixon, L.; Dunbar, D. C.
arXiv
DOI: 10.48550/arxiv.hep-th/9802162

Works referencing / citing this record:

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

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
journal, January 2019

Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu
Journal of High Energy Physics, Vol. 2019, Issue 1
DOI: 10.1007/jhep01(2019)186

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

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
text, January 2019

Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu
Springer
DOI: 10.5167/uzh-172597

Rationalizing Loop Integration
text, January 2018

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

Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
text, January 2018

Golden, John; McLeod, Andrew J.
arXiv
DOI: 10.48550/arxiv.1810.12181

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
text, January 2018

Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu
arXiv
DOI: 10.48550/arxiv.1811.11699

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

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

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

Golden, John; McLeod, Andrew J.; Spradlin, Marcus
arXiv
DOI: 10.48550/arxiv.1902.11286

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

Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron
arXiv
DOI: 10.48550/arxiv.1909.09131

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

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Figures / Tables:

Heptagons from the Steinmann cluster bootstrap journal, February 2017

Supersymmetry, supergravity theories and the dual spinor model journal, April 1977

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

Gluing Ladder Feynman Diagrams into Fishnets journal, August 2017

The Amplituhedron journal, October 2014

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

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

Grassmannian Geometry of Scattering Amplitudes book, May 2016

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

Local spacetime physics from the Grassmannian journal, January 2011

Evidence for a nonplanar amplituhedron journal, June 2016

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

Into the amplituhedron journal, December 2014

Hexagon OPE resummation and multi-Regge kinematics journal, February 2016

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

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

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

Perturbative Quantum Gravity as a Double Copy of Gauge Theory journal, August 2010

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

Nested sums, expansion of transcendental functions, and multiscale multiloop integrals journal, June 2002

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

From d logs to dilogs; the super Yang-Mills MHV amplitude revisited journal, January 2014

Supersymmetric Yang-Mills theories journal, March 1977

Bootstrapping pentagon functions journal, May 2018

New differential equations for on-shell loop integrals journal, April 2011

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

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

OPE for all helicity amplitudes journal, August 2015

First Look at Two-Loop Five-Gluon Scattering in QCD journal, March 2018

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

Uniqueness of two-loop master contours journal, October 2012

Pulling the straps of polygons journal, December 2011

Real-virtual contributions to the inclusive Higgs cross-section at N3LO journal, December 2013

Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs journal, May 1993

Superstring amplitudes and the associator journal, August 2013

Leading singularities and off-shell conformal integrals journal, August 2013

Hexagon Wilson loop OPE and harmonic polylogarithms journal, November 2013

Polylogarithmes multiples uniformes en une variable journal, April 2004

Mellin amplitudes for dual conformal integrals journal, August 2012

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

Bootstrapping an NMHV amplitude through three loops journal, October 2014

The Galois coaction on $\phi^4$ periods journal, January 2017

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

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations journal, December 2016

Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms journal, March 2018

Feynman amplitudes, coaction principle, and cosmic Galois group journal, January 2017

New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level journal, April 2017

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

Gluon scattering amplitudes at strong coupling journal, June 2007

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon journal, March 2015

Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes journal, May 2017

Bootstrapping the three-loop hexagon journal, November 2011

On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences journal, October 1998

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

Azurite : An algebraic geometry based package for finding bases of loop integrals journal, December 2017

Leading singularities and off-shell conformal integrals text, January 2013

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in $ \mathcal{N} = 4 $ SYM journal, June 2011

Dual superconformal invariance, momentum twistors and Grassmannians journal, November 2009

Logarithmic singularities and maximally supersymmetric amplitudes journal, June 2015

The Galois coaction on the electron anomalous magnetic moment journal, January 2018

Harmonic Polylogarithms journal, February 2000

Motivic amplitudes and cluster coordinates journal, January 2014

Hexagonalization of correlation functions journal, January 2017

Optical theorems and steinmann relations journal, April 1975

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM journal, January 2011

A duality for the S matrix journal, March 2010

The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops journal, March 2012

Exponential suppression with four legs and an infinity of loops journal, August 2010

Thermodynamic bubble ansatz journal, September 2011

Uniform asymptotic expansions for hypergeometric functions with large parameters IV journal, October 2014

Generalised Ladders and Single-valued Polylogs text, January 2012

From the holomorphic Wilson loop to ‘d log’ loop-integrands of super-Yang-Mills amplitudes journal, May 2013

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Multi-loop Feynman integrals and conformal quantum mechanics journal, July 2003

Heptagons from the Steinmann Cluster Bootstrap text, January 2017

Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling journal, September 2016

Heptagons from the Steinmann cluster bootstrap
journal, February 2017

Supersymmetry, supergravity theories and the dual spinor model
journal, April 1977

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

Gluing Ladder Feynman Diagrams into Fishnets
journal, August 2017

The Amplituhedron
journal, October 2014

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

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

Grassmannian Geometry of Scattering Amplitudes
book, May 2016

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

Local spacetime physics from the Grassmannian
journal, January 2011

Evidence for a nonplanar amplituhedron
journal, June 2016

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

Into the amplituhedron
journal, December 2014

Hexagon OPE resummation and multi-Regge kinematics
journal, February 2016

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

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

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

Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010

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

Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
journal, June 2002

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

From d logs to dilogs; the super Yang-Mills MHV amplitude revisited
journal, January 2014

Supersymmetric Yang-Mills theories
journal, March 1977

Bootstrapping pentagon functions
journal, May 2018

New differential equations for on-shell loop integrals
journal, April 2011

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

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

OPE for all helicity amplitudes
journal, August 2015

First Look at Two-Loop Five-Gluon Scattering in QCD
journal, March 2018

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

Uniqueness of two-loop master contours
journal, October 2012

Pulling the straps of polygons
journal, December 2011

Real-virtual contributions to the inclusive Higgs cross-section at N3LO
journal, December 2013

Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs
journal, May 1993

Superstring amplitudes and the associator
journal, August 2013

Leading singularities and off-shell conformal integrals
journal, August 2013

Hexagon Wilson loop OPE and harmonic polylogarithms
journal, November 2013

Polylogarithmes multiples uniformes en une variable
journal, April 2004

Mellin amplitudes for dual conformal integrals
journal, August 2012

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

Bootstrapping an NMHV amplitude through three loops
journal, October 2014

The Galois coaction on $\phi^4$ periods
journal, January 2017

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

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
journal, December 2016

Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms
journal, March 2018

Feynman amplitudes, coaction principle, and cosmic Galois group
journal, January 2017

New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
journal, April 2017

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

Gluon scattering amplitudes at strong coupling
journal, June 2007

A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
journal, March 2015

Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes
journal, May 2017

Bootstrapping the three-loop hexagon
journal, November 2011

On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences
journal, October 1998

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

Azurite : An algebraic geometry based package for finding bases of loop integrals
journal, December 2017

Leading singularities and off-shell conformal integrals
text, January 2013

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in $ \mathcal{N} = 4 $ SYM
journal, June 2011

Dual superconformal invariance, momentum twistors and Grassmannians
journal, November 2009

Logarithmic singularities and maximally supersymmetric amplitudes
journal, June 2015

The Galois coaction on the electron anomalous magnetic moment
journal, January 2018

Harmonic Polylogarithms
journal, February 2000

Motivic amplitudes and cluster coordinates
journal, January 2014

Hexagonalization of correlation functions
journal, January 2017

Optical theorems and steinmann relations
journal, April 1975

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM
journal, January 2011

A duality for the S matrix
journal, March 2010

The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops
journal, March 2012

Exponential suppression with four legs and an infinity of loops
journal, August 2010

Thermodynamic bubble ansatz
journal, September 2011

Uniform asymptotic expansions for hypergeometric functions with large parameters IV
journal, October 2014

Generalised Ladders and Single-valued Polylogs
text, January 2012

From the holomorphic Wilson loop to ‘d log’ loop-integrands of super-Yang-Mills amplitudes
journal, May 2013

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Multi-loop Feynman integrals and conformal quantum mechanics
journal, July 2003

Heptagons from the Steinmann Cluster Bootstrap
text, January 2017

Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling
journal, September 2016

From polygons and symbols to polylogarithmic functions
journal, October 2012

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism
journal, May 2018

Graphical functions and single-valued multiple polylogarithms
journal, January 2014

Generalised ladders and single-valued polylogs
journal, February 2013