Holography versus Correspondence principle: eternal Schwarzschild-anti-de Sitter geometry

Abstract

It is shown that the correspondence principle and the holographic principle are incompatible in the background of an eternal Schwarzschild-anti-de Sitter geometry. The argument is based on the observation that algebraic structures of local quantum field and CFT operators are not equivalent. A CFT Hilbert space representation is elaborated which may correspond to the AdS black hole in the dual theory.