OPE for null Wilson loops and open spin chains

Abstract

Maximal helicity-violating scattering amplitudes in N=4 supersymmetric Yang-Mills theory are dual to Wilson loops on closed null polygons. We perform their operator product expansion analysis in two-dimensional kinematics in the soft-collinear approximation which corresponds to the case when some light-cone distances vanish. We construct the expansion in terms of multi-particle "heavy"-light operators, where the "heavy" fields are identified with the Wilson lines defining the OPE channel and the light fields emerge from the curvature of the contour. The correlation function of these define the remainder function. We study the dilatation operator for these operators at one loop order and find that it corresponds to a non-compact open spin chain. This provides an alternative view on elementary excitations propagating on the GKP string at weak coupling, which now correspond to particles traveling along an open spin chain. The factorized structure of the Wilson loop in the soft limit allows one to represent the two-loop correction to the octagon Wilson loop as a convolution formula and find the corresponding remainder function.

10 pages, 2 figures

References in corpus (13)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for 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
• Bootstrapping the three-loop hexagon
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Comments on operators with large spin
• An Operator Product Expansion for Polygonal null Wilson Loops
• Notes on the scattering amplitude / Wilson loop duality
• Logarithmic scaling in gauge/string correspondence
• Integrability of scattering amplitudes in N=4 SUSY
• Analytic Results for MHV Wilson Loops

Cited by in corpus (21)

• 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
• Nonsinglet pentagons and NMHV amplitudes
• Quantum mechanics of null polygonal Wilson loops
• Bethe Ansaetze for GKP strings
• On factorization of multiparticle pentagons
• Hexagons and Correlators in the Fishnet Theory
• From Polygon Wilson Loops to Spin Chains and Back
• Integrability of the evolution equations for heavy-light baryon distribution amplitudes
• Integrability in heavy quark effective theory
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Strong Wilson polygons from the lodge of free and bound mesons
• A note on two-loop superloop
• Supersymmetric quantum mechanics of the flux tube
• Separation of Variables for a flux tube with an end
• Descent equation for superloop and cyclicity of OPE
• ABJM flux-tube and scattering amplitudes
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• An Operator Product Expansion for Form Factors II. Born level
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM