Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space

Abstract

We consider minimal surfaces in three dimensional anti-de-Sitter space that end at the AdS boundary on a polygon given by a sequence of null segments. The problem can be reduced to a certain generalized Sinh-Gordon equation and to SU(2) Hitchin equations. We describe in detail the mathematical problem that needs to be solved. This problem is mathematically the same as the one studied by Gaiotto, Moore and Neitzke in the context of the moduli space of certain supersymmetric theories. Using their results we can find the explicit answer for the area of a surface that ends on an eight-sided polygon. Via the gauge/gravity duality this can also be interpreted as a certain eight-gluon scattering amplitude at strong coupling. In addition, we give fairly explicit solutions for regular polygons.

References in corpus (17)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Comments on operators with large spin
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Generating AdS String Solutions
• A Generalized Scaling Function for AdS/CFT
• Pohlmeyer reduction revisited
• On reduced models for superstrings on AdS_n x S^n
• Moduli Dynamics of AdS_3 Strings
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• Spiky Strings and Spin Chains
• Lectures on Scattering Amplitudes via AdS/CFT
• Moduli spaces of local systems and higher Teichmuller theory

Cited by in corpus (146)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Thermodynamic Bubble Ansatz
• Y-system for Scattering Amplitudes
• Scattering into the fifth dimension of N=4 super Yang-Mills
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• An Operator Product Expansion for Polygonal null Wilson Loops
• Form factors at strong coupling via a Y-system
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• T-systems and Y-systems in integrable systems
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Wall-Crossing in Coupled 2d-4d Systems
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Analytic two-loop form factors in N=4 SYM
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• Exciting the GKP string at any coupling
• Correlation functions of three heavy operators - the AdS contribution
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• TBA equations and resurgent Quantum Mechanics
• Bootstrapping Null Polygon Wilson Loops
• Quantum Sine(h)-Gordon Model and Classical Integrable Equations
• Cluster adjacency beyond MHV
• Moduli Dynamics of AdS_3 Strings
• Simple loop integrals and amplitudes in N=4 SYM
• Notes on supersymmetric Wilson loops on a two-sphere
• Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Analytic Results for MHV Wilson Loops
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• Notes on Euclidean Wilson loops and Riemann Theta functions
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• On holographic three point functions for GKP strings from integrability
• Wave functions and correlation functions for GKP strings from integrability
• Surprises in the AdS algebraic curve constructions - Wilson loops and correlation functions
• Simplicity of Polygon Wilson Loops in N=4 SYM
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states
• Correlation function of null polygonal Wilson loops with local operators
• Semiclassical correlators of three states with large S^5 charges in string theory in AdS_5 x S^5
• Wilson loops and minimal area surfaces in hyperbolic space
• $R^3$ index for four-dimensional $N=2$ field theories
• On the perturbative S-matrix of generalized sine-Gordon models
• Wilson loop OPE, analytic continuation and multi-Regge limit
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Geometric aspects of the ODE/IM correspondence
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• ODE/IM correspondence for the Fateev model
• From Polygon Wilson Loops to Spin Chains and Back
• Wilson loops and Riemann theta functions II
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• Wilson Loops @ 3-Loops in Special Kinematics
• Multichannel Conformal Blocks for Polygon Wilson Loops
• Space-like minimal surfaces in AdS x S
• OPE for Super Loops
• TBA Equations and Quantization Conditions
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• A simple collinear limit of scattering amplitudes at strong coupling
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• ODE/IM correspondence and modified affine Toda field equations
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture
• g-Functions and gluon scattering amplitudes at strong coupling
• Critical values of the Yang-Yang functional in the quantum sine-Gordon model
• T-functions and multi-gluon scattering amplitudes
• Constant mean curvature surfaces in AdS_3
• Hidden Simplicity of Gauge Theory Amplitudes
• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• Some comments on spacelike minimal surfaces with null polygonal boundaries in $Ad{S}_m$
• High Energy String Scattering in AdS
• Segmented Strings in $Ad{S}_3$
• Semiclassical rigid strings with two spins in AdS_5
• On the two-loop hexagon Wilson loop remainder function in N=4 SYM
• Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings
• Double-helix Wilson loops: case of two angular momenta
• Some analytic results for two-loop scattering amplitudes
• Kinks and branes in models with hyperbolic interactions
• Wilson loop remainder function for null polygons in the limit of self-crossing
• Minimal surfaces in AdS space and Integrable systems
• On Elliptic String Solutions in AdS(3) and dS(3)
• Series Solution and Minimal Surfaces in AdS
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Scattering amplitudes at strong coupling for 4K gluons
• The two-loop eight-point amplitude in ABJM theory
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• General Leznov-Savelev solutions for Pohlmeyer reduced AdS${}_5$ minimal surfaces
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• Uplifting Amplitudes in Special Kinematics
• Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS_3
• Giant Magnons in Symmetric Spaces: Explicit N-soliton solutions for CP^n, SU(n) and S^n
• On the mass-coupling relation of multi-scale quantum integrable models
• Minimal area surfaces dual to Wilson loops and the Mathieu equation
• Review of AdS/CFT Integrability, Chapter V.3: Scattering Amplitudes at Strong Coupling
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Cluster algebras in scattering amplitudes with special 2D kinematics
• Hitchin systems in N=2 field theory
• Yangian Symmetry in N=4 super Yang-Mills
• Regular Wilson loops and MHV amplitudes at weak and strong coupling
• Minimal n-Noids in hyperbolic and anti-de Sitter 3-space
• Massive quark scattering at strong coupling from AdS/CFT
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• MHV amplitudes at strong coupling and linearized TBA equations
• Giant Holes
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Irregular Singularities in the H3+ WZW Model
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Separation of Variables for a flux tube with an end
• Minimal area surfaces in AdS${}_3$ through integrability
• Integrability and Wilson loops: the wavy line contour
• Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• Singular Liouville fields and spiky strings in $\rr^{1,2}$ and $SL(2,\rr)$
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Differential equations for multi-loop integrals and two-dimensional kinematics
• Yangian symmetry of light-like Wilson loops
• Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold
• Euclidean Wilson loops and Minimal Area Surfaces in Minkowski AdS3
• AdS String: Classical Solutions and Moduli Dynamics
• Holographic correlation functions of hexagon Wilson loops with one local operator
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Vacuum type space-like string surfaces in AdS_3 x S^3
• Antenna Operator Product Expansion of ABJ(M) Lightlike Polygon Wilson Loop
• A Celestial Description of Planar Super-Yang-Mills Theory
• Spiky Strings with Two Spins in AdS5
• Holographic Calculations of Euclidean Wilson Loop Correlator in Euclidean anti-de Sitter Space
• Multi-trace Correlators from Permutations as Moduli Space
• Novel aspects of integrability for NLSMs in symmetric spaces
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• Meromorphic Painlevé III transcendents and the Joukowski correspondence
• The spectral curve of segmented strings
• Regularity for harmonic maps into certain Pseudo-Riemannian manifolds
• Global existence of the harmonic map heat flow into Lorentzian manifolds
• Elliptic String Solutions in AdS(3) and Elliptic Minimal Surfaces in AdS(4)
• Dilogarithm ladders from Wilson loops
• Gluon scattering amplitudes from gauge/string duality and integrability