skip to main content
OSTI.GOV 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

Journal Article · · Journal of High Energy Physics (Online)
 [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)

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.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1325941
Journal Information:
Journal of High Energy Physics (Online), Vol. 2016, Issue 8; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 49 works
Citation information provided by
Web of Science

References (62)

Magic identities for conformal four-point integrals journal January 2007
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
Pulling the straps of polygons journal December 2011
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
Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions journal August 2014
Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion journal September 2014
OPE for all helicity amplitudes II. Form factors and data analysis journal December 2015
Eliminating spurious poles from gauge-theoretic amplitudes journal May 2013
Motivic amplitudes and cluster coordinates journal January 2014
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
An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal March 2010
The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal May 2010
Classical Polylogarithms for Amplitudes and Wilson Loops journal October 2010
Bootstrapping the three-loop hexagon journal November 2011
Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory journal January 2012
Hexagon functions and the three-loop remainder function journal December 2013
Bootstrapping an NMHV amplitude through three loops journal October 2014
The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory journal June 2014
The four-loop six-gluon NMHV ratio function journal January 2016
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
Analytic results for MHV Wilson loops journal November 2010
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
Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills journal December 2011
Uniqueness of two-loop master contours journal October 2012
BFKL pomeron in the next-to-leading approximation journal June 1998
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
Adjoint BFKL at finite coupling: a short-cut from the collinear limit journal January 2015
Excited hexagon Wilson loops for strongly coupled $ \mathcal{N} = 4 $ SYM journal January 2011
The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory journal January 2013
Single-valued harmonic polylogarithms and the multi-Regge limit journal October 2012
Polylogarithmes multiples uniformes en une variable journal April 2004
Heptagon amplitude in the multi-Regge regime journal October 2014
The BFKL equation, Mueller-Navelet jets and single-valued harmonic polylogarithms journal February 2014
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
Harmonic Polylogarithms journal February 2000
Harmonic Sums, Mellin Transforms and Integrals journal May 1999
Nested sums, expansion of transcendental functions, and multiscale multiloop integrals journal June 2002
Symbolic expansion of transcendental functions journal June 2002
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

Cited By (27)

The Sklyanin bracket and cluster adjacency at all multiplicity journal March 2019
The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy journal July 2019
Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills journal October 2019
Closed strings as single-valued open strings: a genus-zero derivation journal January 2019
Systematics of the multi-Regge three-loop symbol text January 2017
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text January 2018
The Multi-Regge Limit from the Wilson Loop OPE text January 2020
Heptagons from the Steinmann Cluster Bootstrap text January 2017
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy text January 2018
Cluster adjacency and the four-loop NMHV heptagon text January 2019
The Multi-Regge Limit from the Wilson Loop OPE text January 2019
Systematics of the Multi-Regge Three-Loop Symbol text January 2016
All-order amplitudes at any multiplicity in the multi-Regge limit text January 2020
The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy text January 2017
Iterating QCD scattering amplitudes in the high-energy limit text January 2018
Cluster adjacency and the four-loop NMHV heptagon text January 2018
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
Systematics of the Multi-Regge Three-Loop Symbol text January 2016
Heptagons from the Steinmann Cluster Bootstrap text January 2016
Quantum Gravity from Conformal Field Theory text January 2017
Bootstrapping the QCD soft anomalous dimension text January 2017
Rationalizing Loop Integration text January 2018
Closed strings as single-valued open strings: A genus-zero derivation text January 2018
Cluster adjacency and the four-loop NMHV heptagon text January 2018
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity text January 2019
The Multi-Regge Limit from the Wilson Loop OPE text January 2019

Similar Records

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
Journal Article · Thu Jun 21 00:00:00 EDT 2018 · Journal of High Energy Physics (Online) · OSTI ID:1325941

All two-loop MHV remainder functions in multi-Regge kinematics
Journal Article · Mon Jan 21 00:00:00 EST 2019 · Journal of High Energy Physics (Online) · OSTI ID:1325941

Bootstrapping the Three-Loop Hexagon
Journal Article · Tue Nov 08 00:00:00 EST 2011 · JHEP 1111:023,2011 · OSTI ID:1325941