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:
-
- ETH Zurich, Zurich (Switzerland); Istituto Nazionale di Fisica Nucleare (Italy)
- Univ. of Southampton, Southampton (United Kingdom)
- European Organization for Nuclear Research (CERN), Geneva (Switzerland); Univ. catholique de Louvain, Louvain-La-Neuve (Belgium); Fonds National de la Recherche Scientifique (FNRS) (Belgium)
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Univ. catholique de Louvain, Louvain-La-Neuve (Belgium)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), 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. https://doi.org/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. https://doi.org/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 = {Thu Aug 25 00:00:00 EDT 2016},
month = {Thu Aug 25 00:00:00 EDT 2016}
}
Web of Science
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
Gluon scattering amplitudes at strong coupling
journal, June 2007
- Alday, Luis F.; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2007, Issue 06
Conformal properties of four-gluon planar amplitudes and Wilson loops
journal, May 2008
- Drummond, J. M.; Korchemsky, G. P.; Sokatchev, E.
- Nuclear Physics B, Vol. 795, Issue 1-2
MHV amplitudes in super-Yang–Mills and Wilson Loops
journal, May 2008
- Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele
- Nuclear Physics B, Vol. 794, Issue 1-2
Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory
journal, May 2009
- Drummond, James; Henn, Johannes; Plefka, Jan
- Journal of High Energy Physics, Vol. 2009, Issue 05
On planar gluon amplitudes/Wilson loops duality
journal, May 2008
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 795, Issue 1-2
Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
journal, February 2010
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 826, Issue 1-2
Hexagon Wilson loop = six-gluon MHV amplitude
journal, July 2009
- Drummond, J. M.; Henn, J.; Korchemsky, G. P.
- Nuclear Physics B, Vol. 815, Issue 1-2
Comments on gluon scattering amplitudes via AdS/CFT
journal, November 2007
- Alday, Luis F.; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2007, Issue 11
Dual superconformal symmetry, and the amplitude/Wilson loop connection
journal, September 2008
- Berkovits, Nathan; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2008, Issue 09
Notes on the scattering amplitude — Wilson loop duality
journal, July 2011
- Caron-Huot, S.
- Journal of High Energy Physics, Vol. 2011, Issue 7
The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
journal, December 2010
- Mason, Lionel; Skinner, David
- Journal of High Energy Physics, Vol. 2010, Issue 12
Pulling the straps of polygons
journal, December 2011
- Gaiotto, Davide; Maldacena, Juan; Sever, Amit
- Journal of High Energy Physics, Vol. 2011, Issue 12
Exciting the GKP string at any coupling
journal, April 2012
- Basso, B.
- Nuclear Physics B, Vol. 857, Issue 3
Spacetime and Flux Tube -Matrices at Finite Coupling for Supersymmetric Yang-Mills Theory
journal, August 2013
- Basso, Benjamin; Sever, Amit; Vieira, Pedro
- Physical Review Letters, Vol. 111, Issue 9
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
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
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
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
Eliminating spurious poles from gauge-theoretic amplitudes
journal, May 2013
- Hodges, Andrew
- Journal of High Energy Physics, Vol. 2013, Issue 5
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
Cluster algebras II: Finite type classification
journal, May 2003
- Fomin, Sergey; Zelevinsky, Andrei
- Inventiones mathematicae, Vol. 154, Issue 1
Grassmannians and Cluster Algebras
journal, February 2006
- Scott, Joshua S.
- Proceedings of the London Mathematical Society, Vol. 92, Issue 2
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
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
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
Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010
- Goncharov, A. B.; Spradlin, M.; Vergu, C.
- Physical Review Letters, Vol. 105, Issue 15
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
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
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
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
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
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
An analytic result for the two-loop seven-point MHV amplitude in N $$ \mathcal{N} $$ = 4 SYM
journal, August 2014
- Golden, John; Spradlin, Marcus
- Journal of High Energy Physics, Vol. 2014, Issue 8
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
Analytic results for MHV Wilson loops
journal, November 2010
- Heslop, Paul; Khoze, Valentin V.
- Journal of High Energy Physics, Vol. 2010, Issue 11
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
journal, August 2013
- Caron-Huot, Simon; He, Song
- Journal of High Energy Physics, Vol. 2013, Issue 8
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
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
Uniqueness of two-loop master contours
journal, October 2012
- Caron-Huot, Simon; Larsen, Kasper J.
- Journal of High Energy Physics, Vol. 2012, Issue 10
BFKL pomeron in the next-to-leading approximation
journal, June 1998
- Fadin, V. S.; Lipatov, L. N.
- Physics Letters B, Vol. 429, Issue 1-2
Energy scale(s) and next-to-leading BFKL equation
journal, July 1998
- Ciafaloni, Marcello; Camici, Gianni
- Physics Letters B, Vol. 430, Issue 3-4
N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution
journal, December 2009
- Bartels, J.; Lipatov, L. N.; Sabio Vera, A.
- The European Physical Journal C, Vol. 65, Issue 3-4
Implications of multi-Regge limits for the Bern–Dixon–Smirnov conjecture
journal, June 2009
- Brower, Richard C.; Nastase, Horatiu; Schnitzer, Howard J.
- Nuclear Physics B, Vol. 814, Issue 1-2
Analyticity for multi-Regge limits of the Bern–Dixon–Smirnov amplitudes
journal, November 2009
- Brower, Richard C.; Nastase, Horatiu; Schnitzer, Howard J.
- Nuclear Physics B, Vol. 822, Issue 1-2
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
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
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
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
Polylogarithmes multiples uniformes en une variable
journal, April 2004
- Brown, Francis C. S.
- Comptes Rendus Mathematique, Vol. 338, Issue 7
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
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
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
- Fadin, V. S.; Lipatov, L. N.
- Physics Letters B, Vol. 706, Issue 4-5
Equivalence of the Parke-Taylor and the Fadin-Kuraev-Lipatov amplitudes in the high-energy limit
journal, August 1995
- Del Duca, Vittorio
- Physical Review D, Vol. 52, Issue 3
Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA
journal, August 2006
- Fadin, V. S.; Fiore, R.; Kozlov, M. G.
- Physics Letters B, Vol. 639, Issue 2
When does the gluon reggeize?
journal, May 2015
- Caron-Huot, Simon
- Journal of High Energy Physics, Vol. 2015, Issue 5
Harmonic Polylogarithms
journal, February 2000
- Remiddi, E.; Vermaseren, J. A. M.
- International Journal of Modern Physics A, Vol. 15, Issue 05
Harmonic Sums, Mellin Transforms and Integrals
journal, May 1999
- Vermaseren, J. A. M.
- International Journal of Modern Physics A, Vol. 14, Issue 13
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
Symbolic expansion of transcendental functions
journal, June 2002
- Weinzierl, Stefan
- Computer Physics Communications, Vol. 145, Issue 3
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
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
Works referencing / citing this record:
The Sklyanin bracket and cluster adjacency at all multiplicity
journal, March 2019
- Golden, John; McLeod, Andrew J.; Spradlin, Marcus
- Journal of High Energy Physics, Vol. 2019, Issue 3
The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy
journal, July 2019
- Marzucca, Robin; Verbeek, Bram
- Journal of High Energy Physics, Vol. 2019, Issue 7
Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills
journal, October 2019
- Mago, Jorge; Schreiber, Anders; Spradlin, Marcus
- Journal of High Energy Physics, Vol. 2019, Issue 10
Closed strings as single-valued open strings: a genus-zero derivation
journal, January 2019
- Schlotterer, Oliver; Schnetz, Oliver
- Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 4
Systematics of the multi-Regge three-loop symbol
text, January 2017
- Bargheer, Till
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
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
The Multi-Regge Limit from the Wilson Loop OPE
text, January 2020
- Bargheer, Till; Chestnov, Vsevolod; Schomerus, Volker
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Heptagons from the Steinmann Cluster Bootstrap
text, January 2017
- Dixon, Lance J.; Drummond, James; Harrington, Thomas
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
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
Cluster adjacency and the four-loop NMHV heptagon
text, January 2019
- Drummond, James; Foster, Jack; Gürdoğn, Ömer
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Multi-Regge Limit from the Wilson Loop OPE
text, January 2019
- Bargheer, Till; Chestnov, Vsevolod; Schomerus, Volker
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Systematics of the Multi-Regge Three-Loop Symbol
text, January 2016
- Bargheer, Till
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
All-order amplitudes at any multiplicity in the multi-Regge limit
text, January 2020
- Del Duca, V.; Druc, S.; Drummond, J. M.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy
text, January 2017
- Del Duca, Vittorio; Duhr, Claude; Marzucca, Robin
- ETH Zurich
Iterating QCD scattering amplitudes in the high-energy limit
text, January 2018
- Del Duca, Vittorio
- ETH Zurich
Cluster adjacency and the four-loop NMHV heptagon
text, January 2018
- Drummond, James; Foster, Jack; Gürdoğan, Ömer
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
All-order amplitudes at any multiplicity in the multi-Regge limit
text, January 2019
- Del Duca, V.; Druc, S.; Drummond, J. M.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit
text, January 2020
- Del Duca, Vittorio; Druc, S.; Drummond, James M.
- ETH Zurich
Heptagons from the Steinmann Cluster Bootstrap
text, January 2016
- Dixon, Lance J.; Drummond, James; Harrington, Thomas
- arXiv
Quantum Gravity from Conformal Field Theory
text, January 2017
- Aprile, F.; Drummond, J. M.; Heslop, P.
- arXiv
Bootstrapping the QCD soft anomalous dimension
text, January 2017
- Almelid, Øyvind; Duhr, Claude; Gardi, Einan
- arXiv
Rationalizing Loop Integration
text, January 2018
- Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt
- arXiv
Closed strings as single-valued open strings: A genus-zero derivation
text, January 2018
- Schlotterer, Oliver; Schnetz, Oliver
- arXiv
Cluster adjacency and the four-loop NMHV heptagon
text, January 2018
- Drummond, James; Foster, Jack; Gürdoğan, Ömer
- arXiv
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
text, January 2019
- Golden, John; McLeod, Andrew J.; Spradlin, Marcus
- arXiv
The Multi-Regge Limit from the Wilson Loop OPE
text, January 2019
- Bargheer, Till; Chestnov, Vsevolod; Schomerus, Volker
- arXiv