Braneworld holography in Gauss-Bonnet gravity

TL;DR

This paper explores holographic dualities involving Gauss-Bonnet gravity, establishing conditions under which a brane's Friedmann equation matches a CFT-driven cosmology and deriving a Cardy-Verlinde formula in this context.

Contribution

It demonstrates the holographic correspondence for critical branes in Gauss-Bonnet gravity and derives a Cardy-Verlinde formula near the AdS boundary.

Findings

Holography holds for critical branes near the AdS boundary.

No holographic description for non-critical or distant branes.

Derived a Cardy-Verlinde formula for the dual CFT.

Abstract

We investigate holography on an (n-1)-dimensional brane embedded in a background of AdS black holes, in n-dimensional Gauss-Bonnet gravity. We demonstrate that for a critical brane near the AdS boundary, the Friedmann equation corresponds to that of the standard cosmology driven by a CFT dual to the AdS bulk. We show that there is no holographic description for non-critical branes, or when the brane is further away from the AdS boundary. We then derive a Cardy-Verlinde formula for the dual CFT on the critical brane near the boundary. This gives us insight into the remarkable correspondence between Cardy-Verlinde formulae and Friedmann equations in Einstein gravity.