Boundaries of amplituhedra and NMHV symbol alphabets at two loops

Prlina, Igor; Spradlin, Marcus; Stankowicz, James; Stanojevic, Stefan

doi:10.1007/jhep04(2018)049

Title: Boundaries of amplituhedra and NMHV symbol alphabets at two loops

Abstract

In this sequel to [3] we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar N = 4 super-Yang-Mills theory. We explain the connection to on-shell diagrams, which serves as a useful cross-check. Here we determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes.

Authors:

Prlina, Igor ^[1]; Spradlin, Marcus ^[2];

^[3]; Stanojevic, Stefan ^[1]

Brown Univ., Providence, RI (United States). Dept. of Physics
Brown Univ., Providence, RI (United States). Dept. of Physics; Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Brown Univ., Providence, RI (United States). Dept. of Physics; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics

Publication Date:: Tue Apr 10 00:00:00 EDT 2018

Research Org.:: Brown Univ., Providence, RI (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1502077

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: 2018; Journal Issue: 4; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Supersymmetric Gauge Theory

Citation Formats


                    Prlina, Igor, Spradlin, Marcus, Stankowicz, James, and Stanojevic, Stefan. Boundaries of amplituhedra and NMHV symbol alphabets at two loops.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep04(2018)049.

Copy to clipboard


                    Prlina, Igor, Spradlin, Marcus, Stankowicz, James, & Stanojevic, Stefan. Boundaries of amplituhedra and NMHV symbol alphabets at two loops.  United States.  https://doi.org/10.1007/jhep04(2018)049

Copy to clipboard


                    Prlina, Igor, Spradlin, Marcus, Stankowicz, James, and Stanojevic, Stefan. Tue .  
"Boundaries of amplituhedra and NMHV symbol alphabets at two loops".  United States.  https://doi.org/10.1007/jhep04(2018)049.  https://www.osti.gov/servlets/purl/1502077.

Copy to clipboard


                    
@article{osti_1502077,

  title        = {Boundaries of amplituhedra and NMHV symbol alphabets at two loops},

  author       = {Prlina, Igor and Spradlin, Marcus and Stankowicz, James and Stanojevic, Stefan},

  abstractNote = {In this sequel to [3] we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar N = 4 super-Yang-Mills theory. We explain the connection to on-shell diagrams, which serves as a useful cross-check. Here we determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes.},

  doi          = {10.1007/jhep04(2018)049},

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

  number       = 4,

  volume       = 2018,

  place        = {United States},

  year         = {Tue Apr 10 00:00:00 EDT 2018},

  month        = {Tue Apr 10 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/jhep04(2018)049

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 27 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
journal, December 2014

Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy
Physical Review Letters, Vol. 113, Issue 26
DOI: 10.1103/PhysRevLett.113.261603

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

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

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

On analytic properties of vertex parts in quantum field theory
journal, October 1959

Landau, L. D.
Nuclear Physics, Vol. 13, Issue 1
DOI: 10.1016/0029-5582(59)90154-3

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

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

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

Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew
Physical Review Letters, Vol. 117, Issue 24
DOI: 10.1103/PhysRevLett.117.241601

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

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

Bourjaily, Jacob L.; McLeod, Andrew J.; Spradlin, Marcus
Physical Review Letters, Vol. 120, Issue 12
DOI: 10.1103/PhysRevLett.120.121603

Logarithmic singularities and maximally supersymmetric amplitudes
journal, June 2015

Bern, Zvi; Herrmann, Enrico; Litsey, Sean
Journal of High Energy Physics, Vol. 2015, Issue 6
DOI: 10.1007/JHEP06(2015)202

The Amplituhedron
journal, October 2014

Arkani-Hamed, Nima; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2014, Issue 10
DOI: 10.1007/JHEP10(2014)030

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

Looking for a bulk point
journal, January 2017

Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander
Journal of High Energy Physics, Vol. 2017, Issue 1
DOI: 10.1007/JHEP01(2017)013

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

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

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

Star integrals, convolutions and simplices
journal, May 2013

Nandan, Dhritiman; Paulos, Miguel F.; Spradlin, Marcus
Journal of High Energy Physics, Vol. 2013, Issue 5
DOI: 10.1007/JHEP05(2013)105

Into the amplituhedron
journal, December 2014

Arkani-Hamed, Nima; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2014, Issue 12
DOI: 10.1007/JHEP12(2014)182

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

Drummond, J. M.; Papathanasiou, G.; Spradlin, M.
Journal of High Energy Physics, Vol. 2015, Issue 3
DOI: 10.1007/JHEP03(2015)072

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

Uniqueness of two-loop master contours
journal, October 2012

Caron-Huot, Simon; Larsen, Kasper J.
Journal of High Energy Physics, Vol. 2012, Issue 10
DOI: 10.1007/JHEP10(2012)026

Unwinding the amplituhedron in binary
journal, January 2018

Arkani-Hamed, Nima; Thomas, Hugh; Trnka, Jaroslav
Journal of High Energy Physics, Vol. 2018, Issue 1
DOI: 10.1007/JHEP01(2018)016

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

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

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory
journal, March 2016

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia
Journal of High Energy Physics, Vol. 2016, Issue 3
DOI: 10.1007/JHEP03(2016)069

Local integrals for planar scattering amplitudes
journal, June 2012

Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F.
Journal of High Energy Physics, Vol. 2012, Issue 6
DOI: 10.1007/JHEP06(2012)125

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

Grassmannian Geometry of Scattering Amplitudes
book, May 2016

Arkani-Hamed, Nima; Bourjaily, Jacob; Cachazo, Freddy
DOI: 10.1017/CBO9781316091548

On Analytic Properties of Vertex Parts in Quantum Field Theory
book, January 1965

,
Collected Papers of L.D. Landau
DOI: 10.1016/b978-0-08-010586-4.50103-6

Heptagons from the Steinmann Cluster Bootstrap
text, January 2017

Dixon, Lance J.; Drummond, James; Harrington, Thomas
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-00889

Motivic amplitudes and cluster coordinates
text, January 2014

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

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

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

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

Caron-Huot, Simon
arXiv
DOI: 10.48550/arxiv.1105.5606

Bootstrapping the three-loop hexagon
text, January 2011

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

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

Uniqueness of two-loop master contours
text, January 2012

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

Star Integrals, Convolutions and Simplices
text, January 2013

Nandan, Dhritiman; Paulos, Miguel F.; Spradlin, Marcus
arXiv
DOI: 10.48550/arxiv.1301.2500

Logarithmic Singularities and Maximally Supersymmetric Amplitudes
preprint, January 2014

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

Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory
text, January 2015

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia
arXiv
DOI: 10.48550/arxiv.1512.07909

Cluster Functions and Scattering Amplitudes for Six and Seven Points
preprint, January 2015

Harrington, Thomas; Spradlin, Marcus
arXiv
DOI: 10.48550/arxiv.1512.07910

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

Heptagons from the Steinmann Cluster Bootstrap
text, January 2016

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

Unwinding the Amplituhedron in Binary
text, January 2017

Arkani-Hamed, Nima; Thomas, Hugh; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1704.05069

Works referencing / citing this record:

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 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

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

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

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

Rooting out letters: octagonal symbol alphabets and algebraic number theory
journal, February 2020

Bourjaily, Jacob L.; McLeod, Andrew J.; Vergu, Cristian
Journal of High Energy Physics, Vol. 2020, Issue 2
DOI: 10.1007/jhep02(2020)025

A note on letters of Yangian invariants
journal, February 2021

He, Song; Li, Zhenjie
Journal of High Energy Physics, Vol. 2021, Issue 2
DOI: 10.1007/jhep02(2021)155

Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
journal, April 2020

He, Song; Ren, Lecheng; Zhang, Yong
Journal of High Energy Physics, Vol. 2020, Issue 4
DOI: 10.1007/jhep04(2020)140

A double integral of dlog forms which is not polylogarithmic
conference, February 2022

Duhr, Claude; Brown, Francis
Proceedings of MathemAmplitudes 2019: Intersection Theory & Feynman Integrals — PoS(MA2019)
DOI: 10.22323/1.383.0005

How tropical are seven- and eight-particle amplitudes?
text, January 2019

Henke, Niklas; Papathanasiou, Georgios
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-00401

All-loop singularities of scattering amplitudes in massless planar theories
text, January 2018

Prlina, Igor; Spradlin, Marcus; Stanojevic, Stefan
arXiv
DOI: 10.48550/arxiv.1805.11617

Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
text, January 2019

Zhang, Chi; Li, Zhenjie; He, Song
arXiv
DOI: 10.48550/arxiv.1911.01290

Algebraic singularities of scattering amplitudes from tropical geometry
preprint, January 2019

Drummond, James; Foster, Jack; Gürdoğan, Ömer
arXiv
DOI: 10.48550/arxiv.1912.08217

Sign Flip Triangulations of the Amplituhedron
text, January 2020

Kojima, Ryota; Langer, Cameron
arXiv
DOI: 10.48550/arxiv.2001.06473

Symbol Alphabets from Plabic Graphs
text, January 2020

Mago, Jorge; Schreiber, Anders; Spradlin, Marcus
arXiv
DOI: 10.48550/arxiv.2007.00646

The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
text, January 2020

He, Song; Li, Zhenjie; Zhang, Chi
arXiv
DOI: 10.48550/arxiv.2009.11471

Symbol Alphabets from Plabic Graphs II: Rational Letters
text, January 2020

Mago, Jorge; Schreiber, Anders; Spradlin, Marcus
arXiv
DOI: 10.48550/arxiv.2012.15812

Algebraic branch points at all loop orders from positive kinematics and wall crossing
text, January 2021

Herderschee, Aidan
arXiv
DOI: 10.48550/arxiv.2102.03611

Similar Records in DOE PAGES and OSTI.GOV collections:

All-helicity symbol alphabets from unwound amplituhedra

Journal Article Prlina, Igor ; Spradlin, Marcus ; Stankowicz, James ; ... - Journal of High Energy Physics (Online)

Here we review an algorithm for determining the branch points of general amplitudes in planar N = 4 super-Yang-Mills theory from amplituhedra. We demonstrate how to use the recent reformulation of amplituhedra in terms of ‘sign flips’ in order to streamline the application of this algorithm to amplitudes of any helicity. In this way we recover the known branch points of all one-loop amplitudes, and we find an ‘emergent positivity’ on boundaries of amplituhedra.
Cited by 23
https://doi.org/10.1007/jhep05(2018)159

Full Text Available
Symbol alphabets from plabic graphs III: n = 9

Journal Article Mago, J. ; Schreiber, A. ; Spradlin, M. ; ... - Journal of High Energy Physics (Online)

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. In this paper we solve the C Z = 0 matrix equations associated to several cells of the totally non-negative Grassmannian, combining methods of arXiv:2012.15812 for rational letters and arXiv:2007.00646 for algebraic letters. We identify sets of parameterizations of the top cell of G₊(5, 9) for which the solutions produce all of (and only) the cluster variable letters of the 2-loop nine-particle NMHV amplitude, and identify plabic graphs from whichmore »« less
https://doi.org/10.1007/jhep09(2021)002

Full Text Available
Symbol alphabets from plabic graphs

Journal Article Mago, Jorge ; Schreiber, Anders ; Spradlin, Marcus ; ... - Journal of High Energy Physics (Online)

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4, n) as well as certain algebraic functions of cluster variables. In this paper we suggest an algorithm for computing these symbol alphabets from plabic graphs by solving matrix equations of the form C ∙ Z = 0 to associate functions on Gr(m, n) to parameterizations of certain cells of Gr(k, n) indexed by plabic graphs. For m = 4 and n = 8 we show that this association precisely reproduces the 18 algebraic symbol letters of the two-loop NMHV eight-particlemore » amplitude from four plabic graphs.« less
https://doi.org/10.1007/jhep10(2020)128

Full Text Available
Symbol alphabets from tensor diagrams

Journal Article Ren, Lecheng ; Spradlin, Marcus ; Volovich, Anastasia - Journal of High Energy Physics (Online)

We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n-particle amplitudes in planarmore »« less
https://doi.org/10.1007/jhep12(2021)079

Full Text Available
Landau singularities and symbology: One- and two-loop MHV amplitudes in SYM theory

Journal Article Dennen, Tristan ; Spradlin, Marcus ; Volovich, Anastasia - Journal of High Energy Physics (Online)

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N = 4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. Finally, we observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.
Cited by 25
https://doi.org/10.1007/JHEP03(2016)069

Full Text Available

Similar Records

Title: Boundaries of amplituhedra and NMHV symbol alphabets at two loops

Abstract

Citation Formats

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes journal, December 2014

Heptagons from the Steinmann cluster bootstrap journal, February 2017

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

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

On analytic properties of vertex parts in quantum field theory journal, October 1959

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

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

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

Landau singularities from the amplituhedron journal, June 2017

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

Logarithmic singularities and maximally supersymmetric amplitudes journal, June 2015

The Amplituhedron journal, October 2014

Motivic amplitudes and cluster coordinates journal, January 2014

Looking for a bulk point journal, January 2017

Evidence for a nonplanar amplituhedron journal, June 2016

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

Gluon scattering amplitudes at strong coupling journal, June 2007

Star integrals, convolutions and simplices journal, May 2013

Into the amplituhedron journal, December 2014

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

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

Uniqueness of two-loop master contours journal, October 2012

Unwinding the amplituhedron in binary journal, January 2018

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

Bootstrapping the three-loop hexagon journal, November 2011

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory journal, March 2016

Local integrals for planar scattering amplitudes journal, June 2012

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

Grassmannian Geometry of Scattering Amplitudes book, May 2016

On Analytic Properties of Vertex Parts in Quantum Field Theory book, January 1965

Heptagons from the Steinmann Cluster Bootstrap text, January 2017

Motivic amplitudes and cluster coordinates text, January 2014

Classical Polylogarithms for Amplitudes and Wilson Loops text, January 2010

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

Bootstrapping the three-loop hexagon text, January 2011

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

Uniqueness of two-loop master contours text, January 2012

Star Integrals, Convolutions and Simplices text, January 2013

Logarithmic Singularities and Maximally Supersymmetric Amplitudes preprint, January 2014

Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory text, January 2015

Cluster Functions and Scattering Amplitudes for Six and Seven Points preprint, January 2015

Evidence for a Nonplanar Amplituhedron text, January 2015

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

Heptagons from the Steinmann Cluster Bootstrap text, January 2016

Unwinding the Amplituhedron in Binary text, January 2017

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text, January 2018

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text, January 2018

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

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

Rooting out letters: octagonal symbol alphabets and algebraic number theory journal, February 2020

A note on letters of Yangian invariants journal, February 2021

Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals journal, April 2020

A double integral of dlog forms which is not polylogarithmic conference, February 2022

How tropical are seven- and eight-particle amplitudes? text, January 2019

All-loop singularities of scattering amplitudes in massless planar theories text, January 2018

Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations text, January 2019

Algebraic singularities of scattering amplitudes from tropical geometry preprint, January 2019

Sign Flip Triangulations of the Amplituhedron text, January 2020

Symbol Alphabets from Plabic Graphs text, January 2020

The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations text, January 2020

Symbol Alphabets from Plabic Graphs II: Rational Letters text, January 2020

Algebraic branch points at all loop orders from positive kinematics and wall crossing text, January 2021

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
journal, December 2014

Heptagons from the Steinmann cluster bootstrap
journal, February 2017

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

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

On analytic properties of vertex parts in quantum field theory
journal, October 1959

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

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

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

Landau singularities from the amplituhedron
journal, June 2017

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

Logarithmic singularities and maximally supersymmetric amplitudes
journal, June 2015

The Amplituhedron
journal, October 2014

Motivic amplitudes and cluster coordinates
journal, January 2014

Looking for a bulk point
journal, January 2017

Evidence for a nonplanar amplituhedron
journal, June 2016

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

Gluon scattering amplitudes at strong coupling
journal, June 2007

Star integrals, convolutions and simplices
journal, May 2013

Into the amplituhedron
journal, December 2014

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

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

Uniqueness of two-loop master contours
journal, October 2012

Unwinding the amplituhedron in binary
journal, January 2018

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

Bootstrapping the three-loop hexagon
journal, November 2011

Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory
journal, March 2016

Local integrals for planar scattering amplitudes
journal, June 2012

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

Grassmannian Geometry of Scattering Amplitudes
book, May 2016

On Analytic Properties of Vertex Parts in Quantum Field Theory
book, January 1965

Heptagons from the Steinmann Cluster Bootstrap
text, January 2017

Motivic amplitudes and cluster coordinates
text, January 2014

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

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

Bootstrapping the three-loop hexagon
text, January 2011

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

Uniqueness of two-loop master contours
text, January 2012

Star Integrals, Convolutions and Simplices
text, January 2013

Logarithmic Singularities and Maximally Supersymmetric Amplitudes
preprint, January 2014

Landau Singularities and Symbology: One- and Two-loop MHV Amplitudes in SYM Theory
text, January 2015

Cluster Functions and Scattering Amplitudes for Six and Seven Points
preprint, January 2015

Evidence for a Nonplanar Amplituhedron
text, January 2015

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

Heptagons from the Steinmann Cluster Bootstrap
text, January 2016

Unwinding the Amplituhedron in Binary
text, January 2017

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
text, January 2018

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
text, January 2018

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

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

Rooting out letters: octagonal symbol alphabets and algebraic number theory
journal, February 2020

A note on letters of Yangian invariants
journal, February 2021

Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals
journal, April 2020

A double integral of dlog forms which is not polylogarithmic
conference, February 2022

How tropical are seven- and eight-particle amplitudes?
text, January 2019

All-loop singularities of scattering amplitudes in massless planar theories
text, January 2018

Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
text, January 2019

Algebraic singularities of scattering amplitudes from tropical geometry
preprint, January 2019

Sign Flip Triangulations of the Amplituhedron
text, January 2020

Symbol Alphabets from Plabic Graphs
text, January 2020

The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
text, January 2020

Symbol Alphabets from Plabic Graphs II: Rational Letters
text, January 2020

Algebraic branch points at all loop orders from positive kinematics and wall crossing
text, January 2021