Rindler-AdS/CFT

TL;DR

This paper explores the holographic duality between Rindler-AdS space and entangled conformal field theories, deriving thermodynamic properties and causal structures, especially in the tractable AdS_3 case, and discusses dualities involving de Sitter space.

Contribution

It provides a detailed analysis of Rindler-AdS holography, including thermodynamics, causal structure, and dual descriptions in de Sitter space, with explicit calculations in AdS_3.

Findings

Recovered Rindler-AdS thermodynamics from boundary CFT

Derived Rindler temperature and entropy density using the Cardy formula

Demonstrated the CFT's awareness of horizon-crossing events through one-point functions

Abstract

In anti-de Sitter space a highly accelerating observer perceives a Rindler horizon. The two Rindler wedges in AdS_{d+1} are holographically dual to an entangled conformal field theory that lives on two boundaries with geometry R x H_{d-1}. For AdS_3, the holographic duality is especially tractable, allowing quantum-gravitational aspects of Rindler horizons to be probed. We recover the thermodynamics of Rindler-AdS space directly from the boundary conformal field theory. We derive the temperature from the two-point function and obtain the Rindler entropy density precisely, including numerical factors, using the Cardy formula. We also probe the causal structure of the spacetime, and find from the behavior of the one-point function that the CFT "knows" when a source has fallen across the Rindler horizon. This is so even though, from the bulk point of view, there are no local signifiers of the presence of the horizon. Finally, we discuss an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space.