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.

31 pages, 1 Mathematica notebook

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Cited by in corpus (16)

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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