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

Journal Article · 15 March 2015 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP03(2015)072 · OSTI ID:1454720

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; School of Physics & Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom
Université de Savoie, Annecy-le-Vieux Cedex (France). LAPTh, CNRS
Brown Univ., Providence, RI (United States)

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.

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0010010

OSTI ID:: 1454720

Alternate ID(s):: OSTI ID: 22578681

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 3 Vol. 2015; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron arXiv https://doi.org/10.48550/arxiv.1909.09131	text	January 2019
Bootstrapping pentagon functions Chicherin, Dmitry; Henn, Johannes; Mitev, Vladimir Journal of High Energy Physics, Vol. 2018, Issue 5 https://doi.org/10.1007/jhep05(2018)164	journal	May 2018
Gravity on-shell diagrams Herrmann, Enrico; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/jhep11(2016)136	journal	November 2016
Gravity On-shell Diagrams Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1604.03479	text	January 2016
Cluster adjacency and the four-loop NMHV heptagon Drummond, James; Foster, Jack; Gürdoğan, Ömer Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-05809	text	January 2018
Elliptic polylogarithms and Feynman parameter integrals Broedel, Johannes; Duhr, Claude; Dulat, Falko Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)120	journal	May 2019
The Two-Loop Symbol of all Multi-Regge Regions Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker arXiv https://doi.org/10.48550/arxiv.1512.07620	text	January 2015
Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams Bourjaily, Jacob L.; Franco, Sebastián; Galloni, Daniele Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/jhep10(2016)003	journal	October 2016
The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko Journal of High Energy Physics, Vol. 2019, Issue 9 https://doi.org/10.1007/jhep09(2019)061	journal	September 2019
Cluster Adjacency Properties of Scattering Amplitudes in N = 4 Supersymmetric Yang-Mills Theory Drummond, James; Foster, Jack; Gürdoğan, Ömer Physical Review Letters, Vol. 120, Issue 16 https://doi.org/10.1103/physrevlett.120.161601	journal	April 2018
Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills Mago, Jorge; Schreiber, Anders; Spradlin, Marcus Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)099	journal	October 2019
PolyLogTools - Polylogs for the masses Duhr, Claude; Dulat, Falko arXiv https://doi.org/10.48550/arxiv.1904.07279	text	January 2019
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy Del Duca, Vittorio; Druc, Stefan; Drummond, James Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-02259	text	January 2018
Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory Basso, Benjamin; Dixon, Lance J.; Papathanasiou, Georgios Physical Review Letters, Vol. 124, Issue 16 https://doi.org/10.1103/physrevlett.124.161603	journal	April 2020
Landau singularities from the amplituhedron Dennen, T.; Prlina, I.; Spradlin, M. Journal of High Energy Physics, Vol. 2017, Issue 6 https://doi.org/10.1007/jhep06(2017)152	journal	June 2017
Cluster algebras and the subalgebra constructibility of the seven-particle remainder function Golden, John; McLeod, Andrew J. Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/jhep01(2019)017	journal	January 2019
Rationalizing Loop Integration Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt arXiv https://doi.org/10.48550/arxiv.1805.10281	text	January 2018
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy Del Duca, Vittorio; Druc, Stefan; Drummond, James Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-03272	text	January 2018
Heptagons from the Steinmann Cluster Bootstrap Dixon, Lance J.; Drummond, James; Harrington, Thomas Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-00889	text	January 2017
The four-loop six-gluon NMHV ratio function Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J. Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/jhep01(2016)053	journal	January 2016
The double pentaladder integral to all ordersC Caron-Huot, Simon; Dixon, Lance J.; Von Hippel, Matt Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-05437	text	January 2018
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy Del Duca, Vittorio; Druc, Stefan; Drummond, James Journal of High Energy Physics, Vol. 2018, Issue 6 https://doi.org/10.1007/jhep06(2018)116	journal	June 2018
Quantum gravity from conformal field theory Aprile, F.; Drummond, J. M.; Heslop, P. Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/jhep01(2018)035	journal	January 2018
Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series Broedel, Johannes; Duhr, Claude; Dulat, Falko Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/jhep08(2018)014	journal	August 2018
Bootstrapping two-loop Feynman integrals for planar N = 4 $$ \mathcal{N}=4 $$ sYM Henn, Johannes; Herrmann, Enrico; Parra-Martinez, Julio Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/jhep10(2018)059	journal	October 2018
The Double Pentaladder Integral to All Orders Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt arXiv https://doi.org/10.48550/arxiv.1806.01361	text	January 2018
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity Golden, John; McLeod, Andrew J.; Spradlin, Marcus arXiv https://doi.org/10.48550/arxiv.1902.11286	text	January 2019
Bootstrapping the QCD soft anomalous dimension Almelid, Øyvind; Duhr, Claude; Gardi, Einan Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/jhep09(2017)073	journal	September 2017
Bootstrapping the QCD soft anomalous dimension Almelid, Øyvind; Duhr, Claude; Gardi, Einan arXiv https://doi.org/10.48550/arxiv.1706.10162	text	January 2017
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit Del Duca, V.; Druc, S.; Drummond, J. M. Physical Review Letters, Vol. 124, Issue 16 https://doi.org/10.1103/physrevlett.124.161602	journal	April 2020
Prescriptive Unitarity Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1704.05460	text	January 2017
Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2019-01783	text	January 2019
Cluster adjacency and the four-loop NMHV heptagon Drummond, James; Foster, Jack; Gürdoğn, Ömer Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/jhep03(2019)087	journal	March 2019
Rationalizing loop integration Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/jhep08(2018)184	journal	August 2018
Quantum Gravity from Conformal Field Theory Aprile, F.; Drummond, J. M.; Heslop, P. arXiv https://doi.org/10.48550/arxiv.1706.02822	text	January 2017
Full-Color Two-Loop Four-Gluon Amplitude in N = 2 Supersymmetric QCD Duhr, Claude; Johansson, Henrik; Kälin, Gregor Physical Review Letters, Vol. 123, Issue 24 https://doi.org/10.1103/physrevlett.123.241601	journal	December 2019
Boundaries of amplituhedra and NMHV symbol alphabets at two loops Prlina, I.; Spradlin, M.; Stankowicz, J. Journal of High Energy Physics, Vol. 2018, Issue 4 https://doi.org/10.1007/jhep04(2018)049	journal	April 2018
All-Helicity Symbol Alphabets from Unwound Amplituhedra Prlina, Igor; Spradlin, Marcus; Stankowicz, James arXiv https://doi.org/10.48550/arxiv.1711.11507	text	January 2017
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2019-03749	text	January 2019
Evidence for a Nonplanar Amplituhedron Bern, Zvi; Herrmann, Enrico; Litsey, Sean arXiv https://doi.org/10.48550/arxiv.1512.08591	text	January 2015
All-order amplitudes at any multiplicity in the multi-Regge limit Del Duca, V.; Druc, S.; Drummond, J. M. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2020-00194	text	January 2019
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit Del Duca, Vittorio; Druc, S.; Drummond, James M. ETH Zurich https://doi.org/10.3929/ethz-b-000412664	text	January 2020
PolyLogTools — polylogs for the masses Duhr, Claude; Dulat, Falko Journal of High Energy Physics, Vol. 2019, Issue 8 https://doi.org/10.1007/jhep08(2019)135	journal	August 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes Caron-Huot, Simon; Dixon, Lance J.; Dulat, Falko Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2019-02565	text	January 2019
Systematics of the multi-Regge three-loop symbol Bargheer, Till Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-12764	text	January 2017
Cluster adjacency beyond MHV Drummond, James; Foster, Jack; Gürdoğan, Ömer Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/jhep03(2019)086	journal	March 2019
Prescriptive unitarity for non-planar six-particle amplitudes at two loops Bourjaily, Jacob L.; Herrmann, Enrico; Langer, Cameron Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)073	journal	December 2019
Systematics of the Multi-Regge Three-Loop Symbol Bargheer, Till Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2016-02553	text	January 2016
The double pentaladder integral to all orders Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)170	journal	July 2018
Cluster adjacency beyond MHV Drummond, James; Foster, Jack; Gurdogan, Omer arXiv https://doi.org/10.48550/arxiv.1810.08149	text	January 2018
Heptagons from the Steinmann cluster bootstrap Dixon, Lance J.; Drummond, James; Harrington, Thomas Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/jhep02(2017)137	journal	February 2017
Elliptic polylogarithms and Feynman parameter integrals Broedel, Johannes; Duhr, Claude; Dulat, Falko arXiv https://doi.org/10.48550/arxiv.1902.09971	text	January 2019

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