Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills

Abstract

We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in $\mathcal{N}=4$ SYM. We use inversion formula technology in order to reconstruct the CFT data starting from a single discontinuity of the correlator. In the planar strong coupling limit only a finite number of conformal blocks contributes to the discontinuity, which allows us to obtain elegant closed-form expressions for two-point functions of single-trace operators ${\mathcal{O}}_J$ of weight $J=2,3,4$. Our final result passes a number of non-trivial consistency checks: it has the correct discontinuity, it satisfies the superconformal Ward identities, it has a sensible expansion in both defect and bulk OPEs, and is consistent with available results coming from localization. The method is completely algorithmic and can be implemented to calculate correlators of arbitrary weight.

arXiv comment31 pages, 1 Mathematica notebook

References in corpus (56)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Wilson loops in large N field theories
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N
• The Analytic Bootstrap and AdS Superhorizon Locality
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Large Spin Perturbation Theory
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Mellin amplitudes for $Ad{S}_5\times S^5$
• How to Succeed at Holographic Correlators Without Really Trying
• Superconformal Ward Identities and their Solution
• Gravitational S-matrix from CFT dispersion relations
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Wilson Loops in Large N Theories
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Defects in conformal field theory
• Quantum Gravity from Conformal Field Theory
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Bootstrapping the half-BPS line defect
• Unmixing Supergravity
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
• Wilson Loops in N=4 SYM and Fermion Droplets
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Universality at large transverse spin in defect CFT
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Loop corrections for Kaluza-Klein AdS amplitudes
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• More exact predictions of SUSYM for string theory
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• 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${}_1$
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Calogero-Sutherland Approach to Defect Blocks
• All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs
• On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Correlation function of circular Wilson loop with two local operators and conformal invariance
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Regge trajectories for the (2,0) theories

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• A dispersion relation for defect CFT
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Conformal dispersion relations for defects and boundaries
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Analytic bootstrap for magnetic impurities
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Conformal line defects at finite temperature
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• 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
• Holographic Wilson Loop One-point Functions in ABJM Theory