Extensivity Versus Holography in Anti-de Sitter Spaces
  We study the dimensionality manifested in the AdS/CFT correspondence. We show that the dimensionality as expressed by the high temperature behavior of a system has a holographic nature also at the quantum level. The emergence of the AdS black hole as a master field at high temperature leads to the screening of the extra dimensions in its excluded volume. 
J.L.F. Barbon and E. Rabinovici