skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

Abstract

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. In conclusion, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

Authors:
 [1];  [2];  [2];  [3];  [4];  [5];  [4];  [5]
  1. ETH Zurich, Zurich (Switzerland); Istituto Nazionale di Fisica Nucleare (Italy)
  2. Univ. of Southampton, Southampton (United Kingdom)
  3. European Organization for Nuclear Research (CERN), Geneva (Switzerland); Univ. catholique de Louvain, Louvain-La-Neuve (Belgium); Fonds National de la Recherche Scientifique (FNRS) (Belgium)
  4. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  5. Univ. catholique de Louvain, Louvain-La-Neuve (Belgium)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1325941
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: 2016; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; supersymmetric gauge theory; Gauge symmetry; extended supersymmetry

Citation Formats

Del Duca, Vittorio, Druc, Stefan, Drummond, James, Duhr, Claude, Dulat, Falko, Marzucca, Robin, Papathanasiou, Georgios, and Verbeek, Bram. Multi-Regge kinematics and the moduli space of Riemann spheres with marked points. United States: N. p., 2016. Web. doi:10.1007/JHEP08(2016)152.
Del Duca, Vittorio, Druc, Stefan, Drummond, James, Duhr, Claude, Dulat, Falko, Marzucca, Robin, Papathanasiou, Georgios, & Verbeek, Bram. Multi-Regge kinematics and the moduli space of Riemann spheres with marked points. United States. doi:10.1007/JHEP08(2016)152.
Del Duca, Vittorio, Druc, Stefan, Drummond, James, Duhr, Claude, Dulat, Falko, Marzucca, Robin, Papathanasiou, Georgios, and Verbeek, Bram. Thu . "Multi-Regge kinematics and the moduli space of Riemann spheres with marked points". United States. doi:10.1007/JHEP08(2016)152. https://www.osti.gov/servlets/purl/1325941.
@article{osti_1325941,
title = {Multi-Regge kinematics and the moduli space of Riemann spheres with marked points},
author = {Del Duca, Vittorio and Druc, Stefan and Drummond, James and Duhr, Claude and Dulat, Falko and Marzucca, Robin and Papathanasiou, Georgios and Verbeek, Bram},
abstractNote = {We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. In conclusion, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.},
doi = {10.1007/JHEP08(2016)152},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2016,
place = {United States},
year = {2016},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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


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


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


Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
journal, May 2009


On planar gluon amplitudes/Wilson loops duality
journal, May 2008


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


Hexagon Wilson loop = six-gluon MHV amplitude
journal, July 2009


Comments on gluon scattering amplitudes via AdS/CFT
journal, November 2007


Dual superconformal symmetry, and the amplitude/Wilson loop connection
journal, September 2008


Notes on the scattering amplitude — Wilson loop duality
journal, July 2011


The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
journal, December 2010


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

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

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

OPE for super loops
journal, November 2011

  • Sever, Amit; Vieira, Pedro; Wang, Tianheng
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)051

Exciting the GKP string at any coupling
journal, April 2012


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


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

Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions
journal, August 2014

  • Basso, Benjamin; Sever, Amit; Vieira, Pedro
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)085

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


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

  • Basso, Benjamin; Sever, Amit; Vieira, Pedro
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)149

OPE for all helicity amplitudes
journal, August 2015

  • Basso, Benjamin; Caetano, João; Córdova, Lucía
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)018

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

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


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

Iterated path integrals
journal, January 1977


Cluster algebras II: Finite type classification
journal, May 2003


Grassmannians and Cluster Algebras
journal, February 2006


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

  • Brown, Francis C. S.
  • Annales scientifiques de l'École normale supérieure, Vol. 42, Issue 3
  • DOI: 10.24033/asens.2099

An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, March 2010

  • Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.
  • Journal of High Energy Physics, Vol. 2010, Issue 3
  • DOI: 10.1007/JHEP03(2010)099

The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, May 2010

  • Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.
  • Journal of High Energy Physics, Vol. 2010, Issue 5
  • DOI: 10.1007/JHEP05(2010)084

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010


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

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

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

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

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory
journal, June 2014

  • Dixon, Lance J.; Drummond, James M.; Duhr, Claude
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)116

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

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


A two-loop octagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, September 2010

  • Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A.
  • Journal of High Energy Physics, Vol. 2010, Issue 9
  • DOI: 10.1007/JHEP09(2010)015

Analytic results for MHV Wilson loops
journal, November 2010

  • Heslop, Paul; Khoze, Valentin V.
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)035

Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
journal, August 2013


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

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


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

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

BFKL pomeron in the next-to-leading approximation
journal, June 1998


Irreducible part of the next-to-leading BFKL kernel
journal, October 1997


Energy scale(s) and next-to-leading BFKL equation
journal, July 1998


N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution
journal, December 2009


Implications of multi-Regge limits for the Bern–Dixon–Smirnov conjecture
journal, June 2009


Analyticity for multi-Regge limits of the Bern–Dixon–Smirnov amplitudes
journal, November 2009


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


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

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

  • Drummond, J. M.; Papathanasiou, G.
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)185

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

The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory
journal, January 2013

  • Lipatov, Lev; Prygarin, Alexander; Schnitzer, Howard J.
  • Journal of High Energy Physics, Vol. 2013, Issue 1
  • DOI: 10.1007/JHEP01(2013)068

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

The six-point remainder function to all loop orders in the multi-Regge limit
journal, January 2013


Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space
journal, May 2016

  • Broedel, Johannes; Sprenger, Martin
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)055

Polylogarithmes multiples uniformes en une variable
journal, April 2004


The two-loop symbol of all multi-Regge regions
journal, May 2016

  • Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)012

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

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

The Bethe roots of Regge cuts in strongly coupled N = 4 $$ \mathcal{N}=4 $$ SYM theory
journal, July 2015

  • Bartels, J.; Schomerus, V.; Sprenger, M.
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)098

The BFKL equation, Mueller-Navelet jets and single-valued harmonic polylogarithms
journal, February 2014

  • Del Duca, Vittorio; Dixon, Lance J.; Duhr, Claude
  • Journal of High Energy Physics, Vol. 2014, Issue 2
  • DOI: 10.1007/JHEP02(2014)086

BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> SUSY
journal, January 2012


Equivalence of the Parke-Taylor and the Fadin-Kuraev-Lipatov amplitudes in the high-energy limit
journal, August 1995


Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA
journal, August 2006


When does the gluon reggeize?
journal, May 2015


Hedgehog bases for A n cluster polylogarithms and an application to six-point amplitudes
journal, November 2015

  • Parker, Daniel E.; Scherlis, Adam; Spradlin, Marcus
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)136

Harmonic Polylogarithms
journal, February 2000

  • Remiddi, E.; Vermaseren, J. A. M.
  • International Journal of Modern Physics A, Vol. 15, Issue 05
  • DOI: 10.1142/S0217751X00000367

Harmonic Sums, Mellin Transforms and Integrals
journal, May 1999


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

  • Moch, Sven; Uwer, Peter; Weinzierl, Stefan
  • Journal of Mathematical Physics, Vol. 43, Issue 6
  • DOI: 10.1063/1.1471366

Symbolic expansion of transcendental functions
journal, June 2002


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


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


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


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

Hexagon Wilson loop OPE and harmonic polylogarithms
journal, November 2013


    Works referencing / citing this record:

    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