Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence

Abstract

We review, in a self-contained and pedagogical manner, recent developments and techniques for the evaluation of the scattering amplitudes of planar N=4 SYM theory at both weak and strong coupling. Special emphasis is placed on the newly discovered connection between a special class of amplitudes and the expectation values of particular cusped light-like Wilson loops.

100 pages, invited review for Physics Reports

References in corpus (116)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• Wilson loops in large N field theories
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Gluon scattering amplitudes at strong coupling
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Adding flavor to AdS/CFT
• A semi-classical limit of the gauge/string correspondence
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• String Solitons
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Dimensionally Regulated Pentagon Integrals
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Meson Spectroscopy in AdS/CFT with Flavour
• Automatized analytic continuation of Mellin-Barnes integrals
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Multi-loop Amplitudes and Resummation
• Lax Pair for Strings in Lunin-Maldacena Background
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• Calculating Scattering Amplitudes Efficiently
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Dimensionally Regulated One-Loop Integrals
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Structure functions for large $x$ and renormalization of Wilson loops
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• On-Shell Methods in Perturbative QCD
• On the Tree-Level S-Matrix of Yang-Mills Theory
• Comments on operators with large spin
• One-Loop Splitting Amplitudes in Gauge Theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• Aspects of Semiclassical Strings in AdS${}_5$
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Three-Loop Results for Quark and Gluon Form Factors
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Factorization in One-Loop Gauge Theory
• The Large N Limit of $\mathcal{N}=2,1$ Field Theories from Threebranes in F-theory
• Anomalous dimensions of Wilson operators in N=4 SYM theory
• Gauge/string duality for QCD conformal operators
• The Quark Form Factor at Higher Orders
• String Theory and Quark Confinement
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• All-Order Collinear Behavior in Gauge Theories
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Tree Amplitudes in Gauge Theory as Scalar MHV Diagrams
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Large N limit of orbifold field theories
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• A note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature
• Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Simplifying superstring action on AdS_5 x S^5
• Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
• Non-MHV Tree Amplitudes in Gauge Theory
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Sharpening The Leading Singularity
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Generating AdS String Solutions
• Lectures on Twistor Strings and Perturbative Yang-Mills Theory
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• On the Strong Coupling Scaling Dimension of High Spin Operators
• Evolution equation for gluon Regge trajectory
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Light-Cone Wilson Loops and the String/Gauge Correspondence
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Gauge Invariance and Anomalous Dimensions of a Light-Cone Wilson Loop in Light-Like Axial Gauge
• Amplitudes in the beta-deformed Conformal Yang-Mills
• Numerical evaluation of loop integrals
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Infrared Limit of Gluon Amplitudes at Strong Coupling
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Planar quark scattering at strong coupling and universality
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Quark scattering amplitudes at strong coupling
• Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling
• Near BPS Wilson Loop in beta-deformed Theories
• Dressing the Giant Gluon
• Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations
• Gluon scattering in $\mathcal{N}=4$ Super Yang-Mills at finite temperature
• Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle
• Gluon Scattering in Deformed N=4 SYM
• Gluon scattering in N=4 super-Yang-Mills theory from weak to strong coupling
• A Numerical Study of Gluon Scattering Amplitudes in N=4 Super Yang-Mills Theory at Strong Coupling
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle

Cited by in corpus (129)

• Review of AdS/CFT Integrability: An Overview
• Local Integrals for Planar Scattering Amplitudes
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Bootstrapping the three-loop hexagon
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• Scattering into the fifth dimension of N=4 super Yang-Mills
• Bootstrapping an NMHV amplitude through three loops
• Notes on the scattering amplitude / Wilson loop duality
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• All tree-level amplitudes in N=4 SYM
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Exacting N=4 Superconformal Symmetry
• Webs in multiparton scattering using the replica trick
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• On form factors in N=4 sym
• New differential equations for on-shell loop integrals
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Introduction to AdS-CFT
• Diagrammatic Exponentiation for Products of Wilson Lines
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• General properties of multiparton webs: proofs from combinatorics
• Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Moduli Dynamics of AdS_3 Strings
• Simple loop integrals and amplitudes in N=4 SYM
• Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
• Fermionic pentagons and NMHV hexagon
• Quantum integrability and functional equations
• An Introduction to On-shell Recursion Relations
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• The structure of n-point functions of chiral primary operators in N=4 super Yang-Mills at one-loop
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• Dual conformal symmetry at loop level; massive regularization
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes
• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• Correlation function of null polygonal Wilson loops with local operators
• Ultraviolet divergences and factorization for coordinate-space amplitudes
• Symmetries of the N=4 SYM S-matrix
• Superstrings in AdS
• Antipodal Self-Duality for a Four-Particle Form Factor
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• Exponential suppression with four legs and an infinity of loops
• Geometric aspects of the ODE/IM correspondence
• Gauge theory webs and surfaces
• On-shell supersymmetry for massive multiplets
• Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory
• Correlation functions of local composite operators from generalized unitarity
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Prescriptive Unitarity with Elliptic Leading Singularities
• A note on string solutions in AdS_3
• Wilson Loops and QCD/String Scattering Amplitudes
• A super MHV vertex expansion for N=4 SYM theory
• Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Phase transitions in Wilson loop correlator from integrability in global AdS
• Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5
• Lightlike contours with fermions
• Quantum strings in AdS5 x S5 and AdS/CFT duality
• Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory
• Super Non-Abelian T-Duality
• Minimal surfaces in AdS space and Integrable systems
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Series Solution and Minimal Surfaces in AdS
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Non-abelian fermionic T-duality in supergravity
• On the Geometry of Null Polygons in Full N=4 Superspace
• General Leznov-Savelev solutions for Pohlmeyer reduced AdS${}_5$ minimal surfaces
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• Effective String Theory and QCD Scattering Amplitudes
• BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
• The four-loop six-gluon NMHV ratio function
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Fermionic T-duality and U-duality in type II supergravity
• Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling
• The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers
• A Connection between Twistors and Superstring Sigma Models on Coset Superspaces
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• A Note on T-dualities in the Pure Spinor Heterotic String
• WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills
• Massive quark scattering at strong coupling from AdS/CFT
• Deviation from Alday-Maldacena Duality For Wavy Circle
• Antipodal Symmetry of Two-Loop MHV Amplitudes
• A Two-Loop Four-Point Form Factor at Function Level
• Splitting of folded strings in AdS_3
• Semiclassical Regge trajectories of noncritical string and large-N QCD
• Vertex Operators of Super Wilson Loops
• Universal structure of subleading infrared poles at strong coupling
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Super Wilson Loops and Holonomy on Supermanifolds
• Non-Perturbative Four-Point Scattering from First-Quantized Relativistic JWKB
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R^{1,2}
• Algebra of Lax Connection for T-Dual Models
• Theoretical Developments in SUSY
• Wilson Loops and Integrability
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Coulomb Phase Gluon Scattering at Strong Coupling
• A Celestial Description of Planar Super-Yang-Mills Theory
• On classical string solutions in AdS_5 x S^5
• Gluon scattering amplitudes from gauge/string duality and integrability
• On the Baryonic Density and Susceptibilities in a Holographic Model of QCD
• Non-Abelian basis tensor gauge theory
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• A short review on TBA equation and scattering amplitude/Wilson loop duality