Local Quantum Observables in the Anti-deSitter - Conformal QFT Correspondence
K. -H. Rehren
TL;DR
The paper addresses establishing a model-independent AdS-CFT correspondence within quantum field theory by identifying local observable algebras across AdS and its conformal boundary. It develops an algebraic QFT framework and a geometric map between AdS wedges and boundary double-cones, via a bijection $ $ that preserves the symmetry $SO(2,{d})$ and the core locality structure, yielding a common Hilbert space for both descriptions. It shows that AdS observables in finite regions correspond to genuinely extended CFT observables, while CFT fields may emerge as boundary limits, and discusses how crossing symmetry may arise from AdS degrees of freedom. The conclusion reframes holography as a consequence of causal propagation rather than string-theoretic ingredients, offering a path to link AdS dynamics with conformal gauge theories through extended observables and covering-space formulations.
Abstract
Quantum field theory on d+1-dimensional anti-deSitter space-time admits a re-interpretation as a quantum field theory with conformal symmetry on d-dimensional Minkowski space-time. This conjecture originally emerged from string theory considerations. Here, it is proven in a general framework by an explicit identification between the local observables of the two corresponding theories.