Holography versus correspondence principle: Eternal Schwarzschild–anti–de Sitter geometry

摘要

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 conformal field theory (CFT) operators are not equivalent. This implies, in particular, that the bulk CFT must be singular near the black-hole horizon. A CFT Hilbert space representation is elaborated which may correspond to the AdS black hole in the dual theory.