Extensivity versus holography in anti-de Sitter spaces

We study the dimensionality manifested in the AdS/CFT correspondence. We sh ow that the dimensionality as expressed by the high-temperature behaviour o f a system has a holographic nature also at the quantum level. The emergenc e of the AdS black hole as a master field at high temperature leads to the screening of the extra dimensions in its excluded volume. (C) 1999 Elsevier Science B.V.