TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling

Abstract

We compute the minimal area of a string worldsheet ending on two infinite periodic light-like Wilson lines in the AdS${}_3$ boundary, which is dual to the first non-planar correction to the gluon scattering amplitude in $\mathcal{N}=4$ SYM at the strong coupling. Using the connection between the Hitchin system and the thermodynamic Bethe ansatz (TBA) equations, we present an analytic method to compute the minimal area surface and express the non-trivial part of the minimal area in terms of the free energy of the TBA-like equations. Given the cross ratios as inputs, the area computed from the TBA-like equations matches that calculated using the numerical integration.

arXiv comment31 pages, 8 figures

References in corpus (46)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Wilson loops in large N field theories
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Review of AdS/CFT Integrability: An Overview
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Four-dimensional wall-crossing via three-dimensional field 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
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Thermodynamic Bubble Ansatz
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• Y-system for Scattering Amplitudes
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• An Operator Product Expansion for Polygonal null Wilson Loops
• Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
• Form factors at strong coupling via a Y-system
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Correlation functions of three heavy operators - the AdS contribution
• TBA equations and resurgent Quantum Mechanics
• Quantum Sine(h)-Gordon Model and Classical Integrable Equations
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• On the collinear limit of scattering amplitudes at strong coupling
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• On holographic three point functions for GKP strings from integrability
• An Operator Product Expansion for Form Factors
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• TBA Equations and Quantization Conditions
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• TBA equations for the Schrödinger equation with a regular singularity
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Wall-crossing of TBA equations and WKB periods for the third order ODE
• Minimal surfaces in AdS space and Integrable systems
• ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• General Leznov-Savelev solutions for Pohlmeyer reduced AdS${}_5$ minimal surfaces
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• MHV amplitudes at strong coupling and linearized TBA equations
• Color-Kinematics Duality and Dual Conformal Symmetry for A Four-loop Form Factor in N=4 SYM
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills

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