More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve

Abstract

We perform exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $\mathcal{N}=4$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite 't Hooft coupling, and present simple integral expressions in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS${}_2$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. In particular, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.

44 pages + appendices. v2 references added

References in corpus (34)

• Holographic Wilson Loops
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Supersymmetric Wilson loops on S^3
• On gravitational description of Wilson lines
• Hexagonalization of Correlation Functions
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Bootstrapping the half-BPS line defect
• Wilson loops: From four-dimensional SYM to two-dimensional YM
• 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
• A limit for large $R$-charge correlators in $\mathcal{N}=2$ theories
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• Line defects and radiation in $\mathcal{N}=2$ theories
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
• Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories
• Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM
• Towards the exact Bremsstrahlung function of ABJM theory
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• A Semiclassical String Description of Wilson Loop with Local Operators
• Handling Handles. Part II. Stratification and Data Analysis
• Exact Bremsstrahlung functions in ABJM theory
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM
• On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM
• Precision matching of circular Wilson loops and strings in AdS(5)xS(5)
• Spin chain integrability in non-supersymmetric Wilson loops
• Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory
• Universality of Toda equation in $\mathcal{N}=2$ superconformal field theories
• Phase Transition of Anti-Symmetric Wilson Loops in $\mathcal{N}=4$ SYM

Cited by in corpus (40)

• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• N=2 Conformal SYM theories at large N
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Strong coupling expansion of circular Wilson loops and string theories in AdS${}_5\times {\mathrm{S}}^5$ and AdS${}_4\times {\mathrm{CP}}^3$
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• A dispersion relation for defect CFT
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• A review of the AdS/CFT Quantum Spectral Curve
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Mellin amplitudes for 1$d$ CFT
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Functional Equations and Separation of Variables for Exact g-Function
• The topological line of ABJ(M) theory
• On three-point functions in ABJM and the latitude Wilson loop
• Method of images in defect conformal field theories
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Supersymmetric Wilson loops in two dimensions and duality
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Correlation functions of determinant operators in conformal fishnet theory
• 1d Conformal Field Theory and Dispersion Relations
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Exact 1/N expansion of Wilson loop correlators in $\mathcal{N}=4$ Super-Yang-Mills theory
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM