Algebraic Holography

TL;DR

This paper provides a rigorous proof of a one-to-one correspondence between quantum field theories in anti-deSitter space and its conformal boundary, establishing a foundational aspect of holography.

Contribution

It offers a simple, rigorous proof of the algebraic holography correspondence between bulk and boundary quantum field theories.

Findings

Establishes a one-to-one correspondence between bulk and boundary theories.

Identifies observables in wedge and double-cone regions.

Preserves vacuum states and positive-energy representations.

Abstract

A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and positive-energy representations into positive-energy representations.