Limitations of holography

TL;DR

This paper explores the limitations of holography in AdS spaces, revealing two distinct boundary theories and discussing their implications for black hole horizons and dualities.

Contribution

It identifies two different asymptotic expansions in AdS, defining two distinct boundary theories, and analyzes their compatibility and implications for holographic duality.

Findings

Two different boundary theories: global-CFT and Rindler-CFT.

Rindler-CFT cannot capture interior horizon dynamics.

Impossibility of mutually compatible boundary conditions on two boundaries.

Abstract

By studying global AdS using different foliations, global and Rindler-AdS, we show that there are two different asymptotic Fefferman-Graham expansions possible and thus two different definitions of "boundaries". We demonstrate that imposing boundary conditions on the two boundaries is not mutually compatible even when these boundaries are pushed to infinity. Thus, these two procedures define two genuinely distinct theories that we call global-CFT and Rindler-CFT. We show that the Rindler-CFT is not the same as the theory one gets by "Rindlerizing the global-CFT" as described in hep-th/9804085. We conjecture that the Rindler theory is incapable of capturing the dynamics inside the horizon and discuss its implications for the BTZ-CFT duality proposed in hep-th/0106112.