Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling

Abstract

We consider the 1d CFT defined by the half-BPS Wilson line in planar $\mathcal{N}=4$ super Yang-Mills. Using analytic bootstrap methods we derive the four-point function of the super-displacement operator at fourth order in a strong coupling expansion. Via AdS/CFT, this corresponds to the first three-loop correlator in AdS ever computed. To do so we address the operator mixing problem by considering a family of auxiliary correlators. We further extract the anomalous dimension of the lightest non-protected operator and find agreement with the integrability-based numerical result of Grabner, Gromov and Julius.

Minor corrections, matches published version

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• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
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• A tauberian theorem for the conformal bootstrap
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Cited by in corpus (28)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Broken global symmetries and defect conformal manifolds
• Analytic bootstrap for the localized magnetic field
• 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
• Conformal dispersion relations for defects and boundaries
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Mellin amplitudes for 1$d$ CFT
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Dispersive Sum Rules in AdS${}_2$
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory
• Holographic S-fold theories at one loop
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Notes on $n$-point Witten diagrams in AdS${}_2$
• Ironing out the crease
• Conformal line defects at finite temperature
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• 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
• Higher order RG flow on the Wilson line in $\mathcal{N}=4$ SYM
• Beyond AdS${}_2$/dCFT${}_1$: Insertions in Two Wilson Loops