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

TL;DR

This paper demonstrates the incompatibility between the holographic principle and the correspondence principle within eternal Schwarzschild-anti-de Sitter geometries, highlighting differences in algebraic structures and implications for dual CFTs.

Contribution

It reveals fundamental conflicts between holography and correspondence principles in specific black hole backgrounds, proposing a new CFT Hilbert space representation.

Findings

Algebraic structures of quantum fields and CFT operators differ.

Bulk CFT becomes singular near the black-hole horizon.

A new CFT Hilbert space representation is proposed.

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. This implies, in particular, 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.