Y-system for Scattering Amplitudes

Abstract

We compute N=4 Super Yang Mills planar amplitudes at strong coupling by considering minimal surfaces in AdS_5 space. The surfaces end on a null polygonal contour at the boundary of AdS. We show how to compute the area of the surfaces as a function of the conformal cross ratios characterizing the polygon at the boundary. We reduce the problem to a simple set of functional equations for the cross ratios as functions of the spectral parameter. These equations have the form of Thermodynamic Bethe Ansatz equations. The area is the free energy of the TBA system. We consider any number of gluons and in any kinematic configuration.

69 pages, 19 figures, v2: references added, minor additions

References in corpus (24)

• Gluon scattering amplitudes at strong coupling
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• The ODE/IM Correspondence
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Thermodynamic Bubble Ansatz
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Exacting N=4 Superconformal Symmetry
• Generating AdS String Solutions
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Pohlmeyer reduction revisited
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• On reduced models for superstrings on AdS_n x S^n
• Moduli Dynamics of AdS_3 Strings
• Eliminating spurious poles from gauge-theoretic amplitudes
• Symmetries of the N=4 SYM S-matrix
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• B-Physics Observables and Electroweak Precision Data in the CMSSM, mGMSB and mAMSB
• Bihamiltonian structure of the classical superstring in AdS_5 x S**5

Cited by in corpus (158)

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• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Form factors at strong coupling via a Y-system
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• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Harmony of Super Form Factors
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• Exciting the GKP string at any coupling
• On form factors in N=4 sym
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Analytic Solution of Bremsstrahlung TBA
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Correlation functions of three heavy operators - the AdS contribution
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
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• Quantum Sine(h)-Gordon Model and Classical Integrable Equations
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• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
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• Dimer Models and Integrable Systems
• Analytic Results for MHV Wilson Loops
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• On NMHV form factors in N=4 SYM theory from generalized unitarity
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Notes on Euclidean Wilson loops and Riemann Theta functions
• Massless scattering at special kinematics as Jacobi polynomials
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• Fixing the Quantum Three-Point Function
• Surprises in the AdS algebraic curve constructions - Wilson loops and correlation functions
• From Scattering Amplitudes to the Dilatation Generator in N=4 SYM
• Twistor methods for AdS${}_5$
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Geometric aspects of the ODE/IM correspondence
• A note on the eigenvectors of long-range spin chains and their scalar products
• Three-point function of semiclassical states at weak coupling
• From Polygon Wilson Loops to Spin Chains and Back
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• ODE/IM correspondence for the Fateev model
• Multichannel Conformal Blocks for Polygon Wilson Loops
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• TBA Equations and Quantization Conditions
• ODE/IM correspondence and modified affine Toda field equations
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• TBA equations for the Schrödinger equation with a regular singularity
• Integrability of Smooth Wilson Loops in N=4 Superspace
• Critical values of the Yang-Yang functional in the quantum sine-Gordon model
• On strong-coupling correlation functions of circular Wilson loops and local operators
• g-Functions and gluon scattering amplitudes at strong coupling
• T-functions and multi-gluon scattering amplitudes
• The Excited Hexagon Reloaded
• Cross-Order Integral Relations from Maximal Cuts
• Hidden Simplicity of Gauge Theory Amplitudes
• WKB periods for higher order ODE and TBA equations
• Segmented Strings in $Ad{S}_3$
• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• χ-Systems for Correlation Functions
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Nonperturbative enhancement of superloop at strong coupling
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• Wall-crossing of TBA equations and WKB periods for the third order ODE
• Towards NMHV amplitudes at strong coupling
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• ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation
• ODE/IM correspondence for affine Lie algebras: A numerical approach
• High Energy Bounds on Soft N=4 SYM Amplitudes from AdS/CFT
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• 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
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• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
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• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
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• Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces
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• Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS_3
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• A Shortcut to General Tree-level Scattering Amplitudes in N=4 SYM via Integrability
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• An Origin Story for Amplitudes
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• Rotating Wilson loops and open strings in AdS3
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• Liouville Theory, AdS${}_2$ String, and Three-Point Functions
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• Holographic correlation functions of hexagon Wilson loops with one local operator
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Wilson Loops and Integrability
• Multi-trace Correlators from Permutations as Moduli Space
• $\mathcal{N}=4$ polygonal Wilson loops: fermions
• Spiky Strings with Two Spins in AdS5
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Exact quantization and analytic continuation
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• Gravity Amplitudes from a Gaussian Matrix Model
• Gluon scattering amplitudes from gauge/string duality and integrability
• On interpolating anomalous dimension of twist-two operators with general spins
• Wilson Loops and Minimal Surfaces Beyond the Wavy Approximation