Anti-de Sitter no hair, AdS/CFT and the brane-world

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  • 7 February 2001
Abstract
We study the asymptotic behavior of the bulk spacetimes with the negative cosmological constant in the context of the brane-world scenario. We show that, in Euclidean bulk, or in Lorentzian static bulk, some sequences of hypersurfaces with the positive Ricci scalar evolve to the anti-de Sitter spacetime. Based on the AdS/CFT correspondence, we discuss that the positivity of the Ricci scalar is related to the stability of CFT on the brane. The asymptotic local structure of the conformal infinity is also investigated. These features are congenial to (i)the localisation of the gravity on the brane, (ii) the resolving of the mass hierarchy problem and (iii) the sense of the holographic renormalisation group in the warped compactification.

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