Braneworld holography in Gauss-Bonnet gravity

TL;DR

This work extends braneworld holography to Gauss-Bonnet gravity by deriving the bulk GB equations and GB brane junction conditions, and then examining when a holographic description exists for a brane near AdS. It shows that holography persists only for flat, critical branes close to the AdS boundary, and constructs a Cardy-Verlinde–type formula for the dual CFT in this regime, clarifying its relation to the braneworld Friedmann equation in GB gravity. Unlike Einstein gravity, GB holography is not exact in general, so the horizon cross-section does not straightforwardly reproduce the standard cosmology; the CV formula must be used within its holographic limit and with appropriate approximations. The results illuminate how higher curvature corrections alter the deep connections between CFT thermodynamics and cosmological evolution on the brane, and highlight the importance of boundary terms in GB braneworld setups.

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.