Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop

Abstract

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.

31 pages + appendices; v2 References added

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• Universality at large transverse spin in defect CFT
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Exact Correlation Functions in Conformal Fishnet Theory
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• BPS Wilson loops in generic conformal N=2 SU(N) SYM theories
• Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• 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
• Scalar Insertions in Cusped Wilson Loops in the Ladders Limit of Planar N=4 SYM
• Dyson equations for correlators of Wilson loops
• Deformations of the circular Wilson loop and spectral (in)dependence
• Ladder Limit for Correlators of Wilson Loops
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory
• 2d QCD and Integrability, Part I: 't Hooft model
• Defect Localized Entropy: Renormalization Group and Holography
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Multi-trace Correlators from Permutations as Moduli Space
• Boundary bound states and integrable Wilson loops in ABJM
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM