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. Finally, 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.

arXiv comment104 pages, six awesome figures and ancillary files containing the results in Mathematica format

References in corpus (90)

• Harmonic Polylogarithms
• Gluon scattering amplitudes at strong coupling
• BFKL pomeron in the next-to-leading approximation
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Energy Scale(s) and Next-to-leading BFKL Equation
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Cluster algebras II: Finite type classification
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
• Harmonic sums, Mellin transforms and Integrals
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Multiple polylogarithms and mixed Tate motives
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• From polygons and symbols to polylogarithmic functions
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Motivic Amplitudes and Cluster Coordinates
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• An Operator Product Expansion for Polygonal null Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• Uniqueness of two-loop master contours
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Notes on the scattering amplitude / Wilson loop duality
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• - XSummer - Transcendental Functions and Symbolic Summation in Form
• N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Pulling the straps of polygons
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Irreducible part of the next-to-leading BFKL kernel
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Sharpening The Leading Singularity
• Symbolic Expansion of Transcendental Functions
• Exciting the GKP string at any coupling
• BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY
• OPE for all Helicity Amplitudes
• Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Bootstrapping Null Polygon Wilson Loops
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• On the collinear limit of scattering amplitudes at strong coupling
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Iterated amplitudes in the high-energy limit
• BFKL approach and 2->5 MHV amplitude
• Analytic Results for MHV Wilson Loops
• Equivalence of the Parke-Taylor and the Fadin-Kuraev-Lipatov amplitudes in the high-energy limit
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• Star Integrals, Convolutions and Simplices
• Single-valued periods and multiple zeta values
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Hexagon OPE Resummation and Multi-Regge Kinematics
• The BFKL equation, Mueller-Navelet jets and single-valued harmonic polylogarithms
• Wilson loop OPE, analytic continuation and multi-Regge limit
• The six-point remainder function to all loop orders in the multi-Regge limit
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• OPE for Super Loops
• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
• Heptagon Amplitude in the Multi-Regge Regime
• The Two-Loop Symbol of all Multi-Regge Regions
• The Excited Hexagon Reloaded
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes

Cited by in corpus (51)

• PolyLogTools - Polylogs for the masses
• Heptagons from the Steinmann Cluster Bootstrap
• Quantum Gravity from Conformal Field Theory
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Elliptic Feynman integrals and pure functions
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• Bootstrapping the QCD soft anomalous dimension
• Cluster adjacency and the four-loop NMHV heptagon
• Rationalizing Loop Integration
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• How tropical are seven- and eight-particle amplitudes?
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Lifting Heptagon Symbols to Functions
• Closed strings as single-valued open strings: A genus-zero derivation
• All-order amplitudes at any multiplicity in the multi-Regge limit
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Cluster Adjacency for m=2 Yangian Invariants
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• The gluon Regge trajectory at three loops from planar Yang-Mills theory
• The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy
• Multiple zeta values in deformation quantization
• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Amplitude recursions with an extra marked point
• Modular graph forms from equivariant iterated Eisenstein integrals
• The Two-Loop Remainder Function for Eight and Nine Particles
• Anomalous Dimensions from Soft Regge Constants
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• All two-loop MHV remainder functions in multi-Regge kinematics
• Iterating QCD scattering amplitudes in the high-energy limit
• An Origin Story for Amplitudes
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Systematics of the Multi-Regge Three-Loop Symbol
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Clean Single-Valued Polylogarithms
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• One-loop impact factor for the emission of two gluons
• The two-loop Higgs impact factor
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• The Multi-Regge Limit from the Wilson Loop OPE
• Antipodal self-duality of square fishnet graphs
• The long road from Regge poles to the LHC
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• A tale of two Regge limits
• Quark-Gluon Backscattering in the Regge Limit at One-Loop
• A construction of single-valued elliptic polylogarithms
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory