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Title: The two-loop symbol of all multi-Regge regions

Abstract

Here, we study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.

Authors:
 [1];  [2];  [1]
  1. Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., Stanford, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1256308
Report Number(s):
SLAC-PUB-16473
Journal ID: ISSN 1029-8479; PII: 3895; TRN: US1601744
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2016; Journal Issue: 5; 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; 1/N expansion; extended supersymmetry

Citation Formats

Bargheer, Till, Papathanasiou, Georgios, and Schomerus, Volker. The two-loop symbol of all multi-Regge regions. United States: N. p., 2016. Web. doi:10.1007/JHEP05(2016)012.
Bargheer, Till, Papathanasiou, Georgios, & Schomerus, Volker. The two-loop symbol of all multi-Regge regions. United States. doi:10.1007/JHEP05(2016)012.
Bargheer, Till, Papathanasiou, Georgios, and Schomerus, Volker. Mon . "The two-loop symbol of all multi-Regge regions". United States. doi:10.1007/JHEP05(2016)012. https://www.osti.gov/servlets/purl/1256308.
@article{osti_1256308,
title = {The two-loop symbol of all multi-Regge regions},
author = {Bargheer, Till and Papathanasiou, Georgios and Schomerus, Volker},
abstractNote = {Here, we study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.},
doi = {10.1007/JHEP05(2016)012},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 5,
volume = 2016,
place = {United States},
year = {2016},
month = {5}
}

Journal Article:
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Cited by: 6 works
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Works referenced in this record:

A natural ring basis for the shuffle algebra and an application to group schemes
journal, June 1979


Collinear Limit of Scattering Amplitudes at Strong Coupling
journal, December 2014


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

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

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

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


Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
journal, February 2010


MHV amplitudes in super-Yang–Mills and Wilson Loops
journal, May 2008


A Remarkable Representation of the 3 + 2 de Sitter Group
journal, July 1963

  • Dirac, P. A. M.
  • Journal of Mathematical Physics, Vol. 4, Issue 7
  • DOI: 10.1063/1.1704016

Multi-Regge limit of the n-gluon bubble ansatz
journal, November 2012

  • Bartels, J.; Schomerus, V.; Sprenger, M.
  • Journal of High Energy Physics, Vol. 2012, Issue 11
  • DOI: 10.1007/JHEP11(2012)145

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

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

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

Two-loop master integrals for jets: the planar topologies
journal, May 2001


Strong Wilson polygons from the lodge of free and bound mesons
journal, April 2016

  • Bonini, Alfredo; Fioravanti, Davide; Piscaglia, Simone
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)029

Thermodynamic bubble ansatz
journal, September 2011

  • Alday, Luis F.; Gaiotto, Davide; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2011, Issue 9
  • DOI: 10.1007/JHEP09(2011)032

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


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


An analytic result for the two-loop seven-point MHV amplitude in N $$ \mathcal{N} $$ = 4 SYM
journal, August 2014


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

OPE for all helicity amplitudes II. Form factors and data analysis
journal, December 2015

  • Basso, Benjamin; Caetano, João; Córdova, Lucía
  • Journal of High Energy Physics, Vol. 2015, Issue 12
  • DOI: 10.1007/JHEP12(2015)088

Iterated path integrals
journal, January 1977


Cuts in the angular-momentum plane - II
journal, November 1963


Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010


Wilson loop OPE, analytic continuation and multi-Regge limit
journal, October 2014


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

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


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

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

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


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


Excited hexagon Wilson loops for strongly coupled $ \mathcal{N} = 4 $ SYM
journal, January 2011

  • Bartels, J.; Kotanski, J.; Schomerus, V.
  • Journal of High Energy Physics, Vol. 2011, Issue 1
  • DOI: 10.1007/JHEP01(2011)096

Hexagon Wilson loop OPE and harmonic polylogarithms
journal, November 2013


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

Mathematical Aspects of Scattering Amplitudes
conference, November 2015

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

    Works referencing / citing this record:

    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 multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy
    journal, July 2019


    The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy
    journal, July 2019


    The multi-Regge limit from the Wilson loop OPE
    journal, May 2020

    • Bargheer, Till; Chestnov, Vsevolod; Schomerus, Volker
    • Journal of High Energy Physics, Vol. 2020, Issue 5
    • DOI: 10.1007/jhep05(2020)002

    All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
    journal, April 2020