Gluon scattering amplitudes at strong coupling

Abstract

We describe how to compute planar gluon scattering amplitudes at strong coupling in N=4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.

28 pages, harvmac, v4: minor changes

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• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
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• On factorization of multiparticle pentagons
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• Electromagnetic form factors from the fifth dimension
• Null Polygonal Wilson Loops in Full N=4 Superspace
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• Soft Theorems from Effective Field Theory
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• Phase transitions in Wilson loop correlator from integrability in global AdS
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• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
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• TBA for non-perturbative moduli spaces
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• Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• Scattering Amplitudes and Toric Geometry
• Amplituhedra, and Beyond
• Hidden Simplicity of Gauge Theory Amplitudes
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• Segmented Strings in $Ad{S}_3$
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• Reggeization of N=8 Supergravity and N=4 Yang-Mills Theory II
• Gluon Scattering in Deformed N=4 SYM
• Worldsheet scattering for the GKP string
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes
• EPR = ER and Scattering Amplitude as Entanglement Entropy Change
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• Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
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• Extending the nonsingular hyperscaling violating spacetimes
• Integrated negative geometries in ABJM
• Semiclassical rigid strings with two spins in AdS_5
• On the two-loop hexagon Wilson loop remainder function in N=4 SYM
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• Multi-soft theorems in Gauge Theory from MHV Diagrams
• 13th International Conference on Elastic and Diffractive Scattering (Blois Workshop) - Moving Forward into the LHC Era
• The Effective Action of N=8 Supergravity
• Observations on Open and Closed String Scattering Amplitudes at High Energies
• Conformal anomaly of super Wilson loop
• The Coulomb-branch S-matrix from massless amplitudes
• Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5
• An Infinite Family of Elliptic Ladder Integrals
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory
• Double-helix Wilson loops: case of two angular momenta
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• ABJM amplitudes and WL at finite N
• First-quantized N=4 Yang-Mills
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• On Fermionic T-duality of Sigma modes on AdS backgrounds
• Some analytic results for two-loop scattering amplitudes
• Wilson loop remainder function for null polygons in the limit of self-crossing
• A Numerical Study of Gluon Scattering Amplitudes in N=4 Super Yang-Mills Theory at Strong Coupling
• Towards NMHV amplitudes at strong coupling
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• Fourier transforms of UD integrals
• Minimal surfaces in AdS space and Integrable systems
• High Energy Bounds on Soft N=4 SYM Amplitudes from AdS/CFT
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• A defect action for Wilson loops
• Evolution of cusped light-like Wilson loops and geometry of the loop space
• Dual conformal symmetry on the light-cone
• Series Solution and Minimal Surfaces in AdS
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• On Elliptic String Solutions in AdS(3) and dS(3)
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Positivity Sectors and the Amplituhedron
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• MHV amplitudes in N=2 SQCD and in N=4 SYM at one loop
• On the Classification of Residues of the Grassmannian
• All two-loop MHV remainder functions in multi-Regge kinematics
• On the scattering of gluons in the GKP string
• Exact mass-coupling relation for the homogeneous sine-Gordon model
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
• Wilson loops T-dual to Short Strings
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory
• Non-abelian fermionic T-duality in supergravity
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• The two-loop eight-point amplitude in ABJM theory
• General Leznov-Savelev solutions for Pohlmeyer reduced AdS${}_5$ minimal surfaces
• Four-point amplitudes in $\mathcal{N}=2$ SCQCD
• On the Geometry of Null Polygons in Full N=4 Superspace
• Scattering amplitudes at strong coupling for 4K gluons
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
• The four-loop six-gluon NMHV ratio function
• Peculiarities of String Theory on AdS(4) x CP(3)
• On coincidence of Alday-Maldacena-regularized $\sigma$-model and Nambu-Goto areas of minimal surfaces
• Non-planar BCFW Grassmannian Geometries
• Hexagon remainder function in the limit of self-crossing up to three loops
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Effective String Theory and QCD Scattering Amplitudes
• Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS_3
• A Spin Chain from String Theory
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory
• BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
• Multichannel conformal blocks for scattering amplitudes
• Uplifting Amplitudes in Special Kinematics
• Lectures on Three-point Functions in N=4 Supersymmetric Yang-Mills Theory
• Aspects of the N=4 SYM amplitude -- Wilson polygon duality
• Yangian in the Twistor String
• From weak coupling to spinning strings
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• A Connection between Twistors and Superstring Sigma Models on Coset Superspaces
• Maximal transcendental weight contribution of scattering amplitudes
• Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
• Non-Planar On-Shell Diagrams
• Classical Worldsheets for String Scattering on Flat and AdS Spacetime
• A Surprise in the Amplitude/Wilson Loop Duality
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• On the mass-coupling relation of multi-scale quantum integrable models
• Minimal area surfaces dual to Wilson loops and the Mathieu equation
• A Note on Dual MHV Diagrams in N=4 SYM
• Holographic Cusped Wilson loops in $q$-deformed $Ad{S}_5\times S^5$ Spacetime
• Further results for the two-loop Lcc vertex in the Landau gauge
• Strong Wilson polygons from the lodge of free and bound mesons
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Fermionic T-duality and U-duality in type II supergravity
• Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling
• One-dimensional bosonization and the SYK model
• An Origin Story for Amplitudes
• Resummed tree heptagon
• Production cross section of rotating string
• M2-doughnuts
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• One-loop derivation of the Wilson polygon - MHV amplitude duality
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Cluster algebras in scattering amplitudes with special 2D kinematics
• An interplay between static potential and Reggeon trajectory for QCD string
• Wilson Loop diagrams and Positroids
• Regular Wilson loops and MHV amplitudes at weak and strong coupling
• Loops, Polytopes and Splines
• Yangian Symmetry in N=4 super Yang-Mills
• MHV amplitudes at strong coupling and linearized TBA equations
• Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills
• Massive quark scattering at strong coupling from AdS/CFT
• Minimal n-Noids in hyperbolic and anti-de Sitter 3-space
• Giant Holes
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• The twistor Wilson loop and the amplituhedron
• Ironing out the crease
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• Generating string solutions in BTZ
• Deviation from Alday-Maldacena Duality For Wavy Circle
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Supersymmetric Wilson Loops in Diverse Dimensions
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Simplifying instanton corrections to N=4 SYM correlators
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Anatomy of the Amplituhedron
• On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
• A note on two-loop superloop
• Summary of Lepton Photon 2011
• Some Theoretical Developments in SUSY
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• Reggeon exchange from gauge/gravity duality
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
• Dimensional Regularization and Dimensional Reduction in the Light Cone
• A Two-Loop Four-Point Form Factor at Function Level
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Spinning Hexagons
• Supersymmetric quantum mechanics of the flux tube
• Matching gluon scattering amplitudes and Wilson loops in off-shell regularization
• On-shell Supersymmetry and higher-spin amplitudes
• Dual conformal transformations of smooth holographic Wilson loops
• Evolution of Light-Like Wilson Loops with a Self-Intersection in Loop Space
• Holographic Non-local Rotating Observables and their Renormalization
• String Theory: A Framework for Quantum Gravity and Various Applications
• String Theory at LHC Using Top Quarks From String Balls
• Splitting of folded strings in AdS_3
• Illustrations of Integrand-Basis Building at Two Loops
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• Dual conformal invariance in the Regge limit
• Wilson loops in N=6 superspace for ABJM theory
• Superpropagator and superconformal invariants
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Holographic Thermodynamics and Transport of Flavor Fields
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Semiclassical Regge trajectories of noncritical string and large-N QCD
• Descent equation for superloop and cyclicity of OPE
• ABJM flux-tube and scattering amplitudes
• A note on the universality of the Hagedorn behavior of pp-wave strings
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Antipodal self-duality of square fishnet graphs
• The long road from Regge poles to the LHC
• Minimal area surfaces in AdS${}_3$ through integrability
• Wilson Loop Form Factors: A New Duality
• D=3 N=6 superconformal symmetry of AdS_4 x CP^3 superstring
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• Vertex Operators of Super Wilson Loops
• Twistors, strings and supersymmetric gauge theories
• Rational Terms in Theories with Matter
• Singular Liouville fields and spiky strings in $\rr^{1,2}$ and $SL(2,\rr)$
• Impact Factors for Reggeon-Gluon Transitions
• Universal structure of subleading infrared poles at strong coupling
• On anomalous conformal Ward identities for Wilson loops on polygon-like contours with circular edges
• Locally Finite Observables in sYM
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Twisting perturbed parafermions
• Non-commutative holography and scattering amplitudes in a large magnetic background
• Euclidean Wilson loops and Minimal Area Surfaces in Minkowski AdS3
• Differential equations for multi-loop integrals and two-dimensional kinematics
• Twistors, Harmonics and Holomorphic Chern-Simons
• More on Wilson loops for two touching circles
• Lagrangian Insertion in the Light-Like Limit and the Super-Correlators/Super-Amplitudes Duality
• Spectral determinants for twist field correlators
• Yangian symmetry of light-like Wilson loops
• Super Wilson Loops and Holonomy on Supermanifolds
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Analysis of the anomalous-dimension matrix of n-jet operators at 4 loops
• Scattering amplitudes of regularized bosonic strings
• Higher-Point Correlators in N=4 SYM: Generating Functions
• A Note on Loop Amplitudes in QED
• BPS Wilson Loop T-dual to Spinning String in AdS5xS5
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Exceptional conformal anomaly of null polygonal Wilson loops
• Conformal geometry of null hexagons for Wilson loops and scattering amplitudes
• Scattering Amplitudes of QCD String
• Non-Perturbative Four-Point Scattering from First-Quantized Relativistic JWKB
• Antenna Operator Product Expansion of ABJ(M) Lightlike Polygon Wilson Loop
• Vacuum type space-like string surfaces in AdS_3 x S^3
• Conformal Transformations and Strings for an Accelerating Quark-Antiquark Pair in AdS3
• Lectures on twistor theory
• Gluon Scattering Amplitudes in Finite Temperature Gauge/Gravity Dualities
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• Duality symmetry in high energy scattering
• All-order results for soft and collinear gluons
• Holographic correlation functions of hexagon Wilson loops with one local operator
• Algebra of Lax Connection for T-Dual Models
• Flux-Tube Formation and Holographic Tunneling
• On perturbative field theory and twistor string theory
• Light-like Wilson Loops and Cusp Anomalous Dimensions in Non-conformal Gauge Theories
• Yangian Symmetry in Five Dimensions
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• AdS String: Classical Solutions and Moduli Dynamics
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Interplay of Reggeon and photon in pA collisions
• Eternal Inflation with Liouville Cosmology
• A tale of two Regge limits
• Coulomb Phase Gluon Scattering at Strong Coupling
• Doubly elliptic strings on the (anti-)de Sitter manifold
• Jet Physics from Static Charges in AdS
• Eikonal Approach to N=4 SYM Regge Amplitudes in the AdS/CFT Correspondence
• On the Amplitude/Wilson Loop duality in $\mathcal{N}=2$ SCQCD
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD
• Scattering Amplitudes in Gauge Theories
• Discontinuites of BFKL amplitudes and the BDS ansatz
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Topics in Cusped/Lightcone Wilson Loops
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions
• T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory
• Spiky Strings with Two Spins in AdS5
• A Celestial Description of Planar Super-Yang-Mills Theory
• $\mathcal{N}=4$ polygonal Wilson loops: fermions
• Wilson loops for triangular contours with circular edges
• Instanton corrections to the effective action of N=4 SYM
• Theoretical Developments in SUSY
• Wilson Loops and Integrability
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• F-theory amplitudes
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• A coordinate description of partonic processes
• On classical string solutions in AdS_5 x S^5
• The Stratification of Rigidity
• Dilogarithm ladders from Wilson loops
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• Strongly Coupled Heavy and Light Quark Thermal Motion from AdS/CFT
• Hexagon Bootstrap in the Double Scaling Limit
• Duality between Wilson Loops and Scattering Amplitudes
• Brane Tilings as On-shell Diagrams
• Gluon scattering amplitudes from gauge/string duality and integrability
• A note on scattering amplitudes on the moduli space of ABJM
• Novel aspects of integrability for NLSMs in symmetric spaces
• New Variables For Graviton Scattering Amplitudes
• Note About String with Euclidean World-Sheet in AdS(5)xS(5)
• Asymptotic behavior of large polygonal Wilson loops in confining gauge theories
• Conformal Transformations, Rotating String and Effects of angular velocity on Accelerating Quark-Antiquark pair in $Ad{S}_3$
• Yangian-Like Symmetry of Probe-Brane Actions
• Elliptic String Solutions in AdS(3) and Elliptic Minimal Surfaces in AdS(4)