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

Journal Article · · Journal of High Energy Physics (Online)
 [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; School of Physics & Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom
  2. Université de Savoie, Annecy-le-Vieux Cedex (France). LAPTh, CNRS
  3. 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.

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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Cited By (68)

Cluster adjacency and the four-loop NMHV heptagon text January 2018
Cluster adjacency and the four-loop NMHV heptagon text January 2019
Heptagons from the Steinmann Cluster Bootstrap text January 2016
Non-Planar On-Shell Diagrams preprint January 2015
Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops text January 2017
The Sklyanin bracket and cluster adjacency at all multiplicity journal March 2019
Gluing Ladder Feynman Diagrams into Fishnets journal August 2017
The two-loop symbol of all multi-Regge regions text January 2016
Evidence for a nonplanar amplituhedron journal June 2016
Systematics of the Multi-Regge Three-Loop Symbol text January 2016
Six-Gluon amplitudes in planar N$$ \mathcal{N} $$ = 4 super-Yang-Mills theory at six and seven loops journal August 2019
Prescriptive unitarity journal June 2017
The two-loop symbol of all multi-Regge regions journal May 2016
All-helicity symbol alphabets from unwound amplituhedra journal May 2018
Non-planar on-shell diagrams journal June 2015
All-order amplitudes at any multiplicity in the multi-Regge limit text January 2020
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops text January 2019
Bootstrapping pentagon functions journal May 2018
Gravity on-shell diagrams journal November 2016
Gravity On-shell Diagrams text January 2016
Cluster adjacency and the four-loop NMHV heptagon text January 2018
Elliptic polylogarithms and Feynman parameter integrals journal May 2019
The Two-Loop Symbol of all Multi-Regge Regions text January 2015
Stratifying on-shell cluster varieties: the geometry of non-planar on-shell diagrams journal October 2016
The cosmic Galois group and extended Steinmann relations for planar N$$ \mathcal{N} $$ = 4 SYM amplitudes journal September 2019
Cluster Adjacency Properties of Scattering Amplitudes in N = 4 Supersymmetric Yang-Mills Theory journal April 2018
Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills journal October 2019
PolyLogTools - Polylogs for the masses text January 2019
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text January 2018
Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory journal April 2020
Landau singularities from the amplituhedron journal June 2017
Cluster algebras and the subalgebra constructibility of the seven-particle remainder function journal January 2019
Rationalizing Loop Integration text January 2018
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text January 2018
Heptagons from the Steinmann Cluster Bootstrap text January 2017
The four-loop six-gluon NMHV ratio function journal January 2016
The double pentaladder integral to all ordersC text January 2018
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Prescriptive Unitarity text January 2017
Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops text January 2019
Cluster adjacency and the four-loop NMHV heptagon journal March 2019
Rationalizing loop integration journal August 2018
Quantum Gravity from Conformal Field Theory text January 2017
Full-Color Two-Loop Four-Gluon Amplitude in N = 2 Supersymmetric QCD journal December 2019
Boundaries of amplituhedra and NMHV symbol alphabets at two loops journal April 2018
All-Helicity Symbol Alphabets from Unwound Amplituhedra text January 2017
The cosmic Galois group and extended Steinmann relations for planar N $$ \mathcal{N} $$ = 4 SYM amplitudes text January 2019
Evidence for a Nonplanar Amplituhedron text January 2015
All-order amplitudes at any multiplicity in the multi-Regge limit text January 2019
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit text January 2020
PolyLogTools — polylogs for the masses journal August 2019
The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes text January 2019
Systematics of the multi-Regge three-loop symbol text January 2017
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Prescriptive unitarity for non-planar six-particle amplitudes at two loops journal December 2019
Systematics of the Multi-Regge Three-Loop Symbol text January 2016
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Cluster adjacency beyond MHV text January 2018
Heptagons from the Steinmann cluster bootstrap journal February 2017
Elliptic polylogarithms and Feynman parameter integrals text January 2019

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