Holographic Domains of Anti-de Sitter Space

TL;DR

This paper shows that space-like holography can fail in time-dependent AdS brane settings, notably AdS$_4$ branes in AdS$_5$, where bulk volumes diverge while brane areas remain finite. By adopting the covariant light-sheet holographic principle, the authors define brane holographic domains and use causal diamonds to map bulk excitations to CFT shells on the brane, explaining how holographic images evanesce when excitations exit the domain. In the AdS$_4$/AdS$_5$ system, the bulk splits into two holographic sectors, with a boundary coupling that permits a complete, unitary description across the full AdS$_5$ space. The work provides a consistent, time-independent framework for holography in braneworlds and offers new insight into gravity localization and boundary dynamics in higher-dimensional AdS geometries.

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.