Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations

Abstract

We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of N=4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux. This involves several types of two-point functions which are vanishing in the theory without the defect, such as two-point functions of operators of unequal conformal dimension. We furthermore exploit the operator product expansion (OPE) and the boundary operator expansion (BOE), which form the basis of the boundary conformal bootstrap equations, to extract conformal data both about the defect CFT and about N=4 SYM theory without the defect. From the knowledge of the one- and two-point functions of the defect theory, we extract certain structure constants of N=4 SYM theory using the (bulk) OPE and constrain certain bulk-bulk-to-boundary couplings using the BOE. The extraction of the former relies on a non-trivial, polynomial k dependence of the one-point functions, which we explicitly demonstrate. In addition, it requires the knowledge of the one-point functions of SU$(2)$ descendant operators, which we likewise explicitly determine.

34 pages, 2 figures

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• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
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Cited by in corpus (28)

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• Analytic Bootstrap for Boundary CFT
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• Spin Chain Overlaps and the Twisted Yangian
• Analytic bootstrap for the localized magnetic field
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• One-point functions in AdS/dCFT
• Integrable domain walls in ABJM theory
• Conformal dispersion relations for defects and boundaries
• A Quantum Check of Non-Supersymmetric AdS/dCFT
• Supersymmetric D3/D5 for massive defects on curved space
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• String integrability of the ABJM defect
• Volume complexity for the non-supersymmetric Janus AdS${}_5$ geometry
• Quark-antiquark potential in defect conformal field theory
• A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$
• On actions for (entangling) surfaces and DCFTs
• Holographic correlators of semiclassical states in defect CFTs
• Conformal line defects at finite temperature
• Circular Wilson loops in defect $\mathcal{N}$=4 SYM: phase transitions, double-scaling limits and OPE expansion
• B-type anomaly coefficients for the D3-D5 domain wall
• More on Boundary Holographic Witten Diagrams
• One-point functions in $\beta$-deformed N = 4 SYM with defect
• Holographic 2-Point Functions in the Pseudo-Conformal Universe
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain