Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions

Abstract

We consider light-like Wilson loops with hexagonal geometry in the planar limit of N=4 Super-Yang-Mills theory. Within the Operator-Product-Expansion framework these loops receive contributions from all states that can propagate on top of the colour flux tube sourced by any two opposite edges of the loops. Of particular interest are the two-particle contributions. They comprise virtual effects like the propagation of a pair of scalars, fermions, and gluons, on top of the flux tube. Each one of them is thoroughly discussed in this paper. Our main result is the prediction of all the twist-2 corrections to the expansion of the dual 6-gluons MHV amplitude in the near-collinear limit at finite coupling. At weak coupling, our result was recently used by Dixon, Drummond, Duhr and Pennington to predict the full amplitude at four loops. At strong coupling, it allows us to make contact with the classical string description and to recover the (previously elusive) AdS(3) mode from the continuum of two-fermion states. More generally, the two-particle contributions serve as an exemplar for all the multi-particle corrections.

40 pages + 37 pages of appendices, 24 figures, no footnotes

References in corpus (29)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Comments on operators with large spin
• On String S-matrix, Bound States and TBA
• An Operator Product Expansion for Polygonal null Wilson Loops
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Notes on the scattering amplitude / Wilson loop duality
• Logarithmic scaling in gauge/string correspondence
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Measurement of the charm fragmentation function in D* photoproduction at HERA
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• On the Strong Coupling Scaling Dimension of High Spin Operators
• A Generalized Scaling Function for AdS/CFT
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Quantum mechanics of null polygonal Wilson loops
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• On Yangian-invariant regularisation of deformed on-shell diagrams in N=4 super-Yang-Mills theory
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• The nested SU(N) off-shell Bethe ansatz and exact form factors
• The Excited Hexagon Reloaded
• Cluster Polylogarithms for Scattering Amplitudes
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Collinear and Regge behavior of 2 -> 4 MHV amplitude in N = 4 super Yang-Mills theory

Cited by in corpus (92)

• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Gluing Ladders into Fishnets
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• OPE for all Helicity Amplitudes
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• On the collinear limit of scattering amplitudes at strong coupling
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• The Double Pentaladder Integral to All Orders
• A Three-Point Form Factor Through Five Loops
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Cluster adjacency beyond MHV
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Nonsinglet pentagons and NMHV amplitudes
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Fermionic pentagons and NMHV hexagon
• How tropical are seven- and eight-particle amplitudes?
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Folding Amplitudes into Form Factors: An Antipodal Duality
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• Lifting Heptagon Symbols to Functions
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• All-order amplitudes at any multiplicity in the multi-Regge limit
• An Operator Product Expansion for Form Factors
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Antipodal Self-Duality for a Four-Particle Form Factor
• Three-Point Functions and su(1|1) Spin Chains
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Evaluating the 6-point Remainder Function Near the Collinear Limit
• On factorization of multiparticle pentagons
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Matrix pentagons
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
• Integrability of Smooth Wilson Loops in N=4 Superspace
• The Two-Loop Remainder Function for Eight and Nine Particles
• Heptagon Amplitude in the Multi-Regge Regime
• Cross-Order Integral Relations from Maximal Cuts
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• Hexagon POPE: effective particles and tree level resummation
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• Worldsheet scattering for the GKP string
• Nonperturbative enhancement of superloop at strong coupling
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
• Towards NMHV amplitudes at strong coupling
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• All two-loop MHV remainder functions in multi-Regge kinematics
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• On the scattering of gluons in the GKP string
• Multichannel conformal blocks for scattering amplitudes
• Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model
• The four-loop six-gluon NMHV ratio function
• Non-Planar On-Shell Diagrams
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Strong Wilson polygons from the lodge of free and bound mesons
• Resummed tree heptagon
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• A Two-Loop Four-Point Form Factor at Function Level
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Supersymmetric quantum mechanics of the flux tube
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• ABJM flux-tube and scattering amplitudes
• Descent equation for superloop and cyclicity of OPE
• The Multi-Regge Limit from the Wilson Loop OPE
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Quantum dispersion relations for the $Ad{S}_4\times C{P}^3$ GKP string
• Antenna Operator Product Expansion of ABJ(M) Lightlike Polygon Wilson Loop
• An Operator Product Expansion for Form Factors II. Born level
• $\mathcal{N}=4$ polygonal Wilson loops: fermions
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
• Uniform Gauge for D1-brane in General Background
• Hexagon Bootstrap in the Double Scaling Limit