Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization

Abstract

We compute correlation functions of protected primaries on the $1/2$-BPS Wilson loop in $\mathcal{N}$ = 4 super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present explicit formulae for general two-, three- and four-point functions. The results for two- and three-point functions as well as four-point functions in special kinematics are in perfect agreement with the localization computation performed in arXiv:1802.05201. We then analyze the results in view of the integrability-based approach called "hexagonalization", which was introduced previously to study the correlation functions in the absence of the Wilson loop. In this approach, one decomposes the correlator into fundamental building blocks called "hexagons", and glues them back together by summing over the intermediate states. Through the comparison, we conjecture that the correlation functions on the Wilson loop can be computed by contracting hexagons with boundary states, where each boundary state represents a segment of the Wilson loop. As a byproduct, we make predictions for the large-charge asymptotics of the structure constants on the Wilson loop. Along the way, we refine the conjecture for the integrability-based approach to the general non-BPS structure constants on the Wilson loop, proposed originally in arXiv:1706.02989.

v3 Typos corrected

References in corpus (53)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Review of AdS/CFT Integrability: An Overview
• AdS Dual of the Critical O(N) Vector Model
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Integrability for the Full Spectrum of Planar AdS/CFT
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Quantum spectral curve for AdS_5/CFT_4
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Hexagonalization of Correlation Functions
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Integrable open spin chains from giant gravitons
• Integrable Wilson loops
• Bootstrapping the half-BPS line defect
• Tessellating cushions: four-point functions in N=4 SYM
• Reflecting magnons
• ABJ Triality: from Higher Spin Fields to Strings
• Correlation functions of three heavy operators - the AdS contribution
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• Integrable Open Spin Chains in Defect Conformal Field Theory
• The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Veneziano Amplitude of Vasiliev Theory
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Three-point functions in the SU(2) sector at strong coupling
• The structure of n-point functions of chiral primary operators in N=4 super Yang-Mills at one-loop
• Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter
• Handling Handles. Part II. Stratification and Data Analysis
• Reflecting magnons from D7 and D5 branes
• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• On four-point functions and integrability in N=4 SYM: from weak to strong coupling
• On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM
• Spin chain integrability in non-supersymmetric Wilson loops
• Classical Integrability for Three-point Functions: Cognate Structure at Weak and Strong Couplings
• Y-system for Y=0 brane in planar AdS/CFT
• Structure constants of operators on the Wilson loop from integrability
• Deformations of the circular Wilson loop and spectral (in)dependence

Cited by in corpus (14)

• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Broken global symmetries and defect conformal manifolds
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Mellin amplitudes for 1$d$ CFT
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• On three-point functions in ABJM and the latitude Wilson loop
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills