Holographic Domains of Anti-de Sitter Space

TL;DR

This paper resolves a paradox in holographic duality for AdS_4 branes in AdS_5 by employing a covariant holographic principle, clarifying how four-dimensional gravity emerges from the bulk and how dual CFT excitations behave.

Contribution

It demonstrates the necessity of a covariant holographic approach for AdS_4/AdS_5 models and provides methods to locate dual CFT excitations and understand their dynamics.

Findings

Resolved the holographic paradox with covariant principles.

Showed light-ray intersections match gravity localization.

Linked bulk particle exit to holographic image movement.

Abstract

An AdS_4 brane embedded in AdS_5 exhibits the novel feature that a four-dimensional graviton is localized near the brane, but the majority of the infinite bulk away from the brane where the warp factor diverges does not see four-dimensional gravity. A naive application of the holographic principle from the point of view of the four-dimensional observer would lead to a paradox; a global holographic mapping would require infinite entropy density. In this paper, we show that this paradox is resolved by the proper covariant formulation of the holographic principle. This is the first explicit example of a time-independent metric for which the spacelike formulation of the holographic principle is manifestly inadequate. Further confirmation of the correctness of this approach is that light-rays leaving the brane intersect at the location where we expect four-dimensional gravity to no longer dominate. We also present a simple method of locating CFT excitations dual to a particle in the bulk. We find that the holographic image on the brane moves off to infinity precisely when the particle exits the brane's holographic domain. Our analysis yields an improved understanding of the physics of the AdS_4/AdS_5 model.