A comment on the dual field in the AdS-CFT correspondence

Abstract

In the perturbative AdS-CFT correspondence, the dual field whose source are the prescribed boundary values of a bulk field in the functional integral, and the boundary limit of the quantized bulk field are the same thing. This statement is due to the fact that Witten graphs are boundary limits of the corresponding Feynman graphs for the bulk fields, and hence the dual conformal correlation functions are limits of bulk correlation functions. This manifestation of duality is analyzed in terms of the underlying functional integrals of different structure.

15 pages, v2 substantially revised and extended to vector fields, references added

Cited by in corpus (21)

• States and Boundary Terms: Subtleties of Lorentzian AdS/CFT
• Asymptotic Flatness, Little String Theory, and Holography
• Intertwining Operator Realization of anti de Sitter Holography
• On the algebraic quantization of a massive scalar field in anti-de-Sitter spacetime
• Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)
• Generalized Wentzell boundary conditions and quantum field theory
• The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes
• A critical look at 50 years particle theory from the perspective of the crossing property
• Non-linear Laplace equation, de Sitter vacua and information geometry
• AdS/CFT correspondence in the Euclidean context
• A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes
• Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II (The search of the interface between QFT and QG)
• String theory and the crisis of particle physics II or the ascent of metaphoric arguments
• String theory, the crisis in particle physics and the ascent of metaphoric arguments
• String theory deconstructed
• Quantum field theory on manifolds with a boundary
• Protecting the conformal symmetry via bulk renormalization on Anti deSitter space
• A triviality result in the AdS/CFT correspondence for Euclidean quantum fields with exponential interaction
• AdS/CFT and its proof
• Constructing CFTs from AdS flows
• Finite-coupling spectrum of O(N) model in AdS