An Operator Product Expansion for Polygonal null Wilson Loops

Abstract

We consider polygonal Wilson loops with null edges in conformal gauge theories. We derive an OPE-like expansion when several successive lines of the polygon are becoming aligned. The limit corresponds to a collinear, or multicollinear, limit and we explain the systematics of all the subleading corrections, going beyond the leading terms that were previously considered. These subleading corrections are governed by excitations of high spin operators, or excitations of a flux tube that goes between two Wilson lines. The discussion is valid for any conformal gauge theory, for any coupling and in any dimension. For N=4 super Yang Mills we check this expansion at strong coupling and at two loops at weak coupling . We also make predictions for the remainder function at higher loops. In the process, we also derived a new version for the TBA integral equations that determine the strong coupling answer and present the area as the associated Yang-Yang functional.

48 pages, 12 figures, harvmac. v2 fixed a small issue regarding divergences

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Cited by in corpus (143)

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• Motivic Amplitudes and Cluster Coordinates
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Bootstrapping an NMHV amplitude through three loops
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Heptagons from the Steinmann Cluster Bootstrap
• 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
• From correlation functions to Wilson loops
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Hexagonalization of Correlation Functions
• Wall-Crossing in Coupled 2d-4d Systems
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Pulling the straps of polygons
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Integrable Wilson loops
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Harmony of Super Form Factors
• Gluing Ladders into Fishnets
• Multipoint Conformal Blocks in the Comb Channel
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• More on gapped Goldstones at finite density: More gapped Goldstones
• OPE for all Helicity Amplitudes
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Structure constants at wrapping order
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• On the collinear limit of scattering amplitudes at strong coupling
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Cluster adjacency beyond MHV
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin
• Nonsinglet pentagons and NMHV amplitudes
• Simple loop integrals and amplitudes in N=4 SYM
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Fermionic pentagons and NMHV hexagon
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• How tropical are seven- and eight-particle amplitudes?
• BFKL approach and 2->5 MHV amplitude
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Quantum mechanics of null polygonal Wilson loops
• Notes on Euclidean Wilson loops and Riemann Theta functions
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• MHV diagrams in twistor space and the twistor action
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Antipodal Self-Duality for a Four-Particle Form Factor
• Bethe Ansaetze for GKP strings
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• On factorization of multiparticle pentagons
• The role of leading twist operators in the Regge and Lorentzian OPE limits
• Wilson loops and minimal area surfaces in hyperbolic space
• Subleading Regge limit from a soft anomalous dimension
• Wilson loop OPE, analytic continuation and multi-Regge limit
• The six-point remainder function to all loop orders in the multi-Regge limit
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• From Polygon Wilson Loops to Spin Chains and Back
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• Wilson Loops @ 3-Loops in Special Kinematics
• Wilson loops and Riemann theta functions II
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• Multichannel Conformal Blocks for Polygon Wilson Loops
• OPE for Super Loops
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• The Wilson Loop -- Large Spin OPE Dictionary
• OPE for null Wilson loops and open spin chains
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• The Wilson-loop $d\log$ representation for Feynman integrals
• Bootstrapping a Two-Loop Four-Point Form Factor
• The Two-Loop Remainder Function for Eight and Nine Particles
• Integrability of Smooth Wilson Loops in N=4 Superspace
• The Two-Loop Symbol of all Multi-Regge Regions
• Null Polygonal Wilson Loops in Full N=4 Superspace
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Hexagon POPE: effective particles and tree level resummation
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Worldsheet scattering for the GKP string
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Some analytic results for two-loop scattering amplitudes
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Wilson loop remainder function for null polygons in the limit of self-crossing
• On the origin of the correspondence between classical and quantum integrable theories
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• ABJM quantum spectral curve and Mellin transform
• $T$, $Q$ and periods in $SU(3)$ $\mathcal{N}=2$ SYM
• All two-loop MHV remainder functions in multi-Regge kinematics
• On the scattering of gluons in the GKP string
• Wilson loops T-dual to Short Strings
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Uplifting Amplitudes in Special Kinematics
• Green-Schwarz superstring on the lattice
• Scattering of Giant Holes
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
• Strong Wilson polygons from the lodge of free and bound mesons
• Minimal area surfaces dual to Wilson loops and the Mathieu equation
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• An Origin Story for Amplitudes
• Amplitudes from anomalous superconformal symmetry
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• MHV amplitudes at strong coupling and linearized TBA equations
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• A Two-Loop Four-Point Form Factor at Function Level
• Spinning Hexagons
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• On analytical perturbative solution of ABJM quantum spectral curve
• ABJM flux-tube and scattering amplitudes
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• The Multi-Regge Limit from the Wilson Loop OPE
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Differential equations for multi-loop integrals and two-dimensional kinematics
• Euclidean Wilson loops and Minimal Area Surfaces in Minkowski AdS3
• Yangian symmetry of light-like Wilson loops
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Large spin expansion of the wrapping correction to Freyhult-Rej-Zieme twist operators
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• An Operator Product Expansion for Form Factors II. Born level
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• Hexagon Bootstrap in the Double Scaling Limit
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• Quantum TBA for refined BPS indices
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM