A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes

TL;DR

This paper demonstrates a holographic mechanism for non-interacting Klein-Gordon fields on asymptotically anti-de Sitter spacetimes, showing boundary-localized observable algebras are subalgebras of boundary algebras, based on unique continuation theorems.

Contribution

It introduces a new holographic framework for classical fields on AdS spacetimes using unique continuation at the boundary.

Findings

Boundary-localized algebras are subalgebras of boundary algebras.

Holography for classical fields is established in this setting.

Unique continuation theorems are key to the proof.

Abstract

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.