A covariant approach to braneworld holography

TL;DR

This paper develops a covariant framework for holography in braneworld scenarios, showing that the bulk Weyl tensor can be replaced by holographic energy-momentum on the brane, applicable to non-trivial bulk spacetimes.

Contribution

It extends holographic correspondence to all co-dimension one branes in complex bulk geometries using a covariant approach.

Findings

Bulk Weyl tensor can be replaced by holographic energy-momentum.

Exact correspondence holds for all orders in brane energy-momentum.

Framework applies to non-maximally symmetric bulk spacetimes.

Abstract

Exact holography for cosmological branes in an AdS-Schwarzschild bulk was first introduced in hep-th/0204218. We extend this notion to include all co-dimension one branes moving in non-trivial bulk spacetimes. We use a covariant approach, and show that the bulk Weyl tensor projected on to the brane can always be traded in for "holographic" energy-momentum on the brane. More precisely, a brane moving in a non-maximally symmetric bulk has exactly the same geometry as a brane moving in a maximally symmetric bulk, so long as we include the holographic fields on the brane. This correspondence is exact in that it works to all order in the brane energy-momentum tensor.