A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes
Résumé
In the setting of non-interacting Klein–Gordon fields on asymptotically anti-de Sitter spacetimes, we show that algebras of observables localized in a neighborhood of the boundary are subalgebras of a boundary algebra. The underlying mechanism is directly related to holography for classical fields. In particular, the proof relies on unique continuation theorems at the conformal boundary.