On geodesic propagators and black hole holography

TL;DR

This paper investigates how non-local field theory quantities can probe the interior of black holes in AdS/CFT duality, demonstrating that propagators reveal information about horizons and spacetime regions behind them, with results matching toy models.

Contribution

It extends the understanding of black hole interior probing via propagators in AdS/CFT, specifically for BTZ and single-exterior black holes, and compares results with toy models.

Findings

Propagators reproduce vacuum states in black hole spacetimes.

Remarkable agreement with toy model CFT results.

Insights into causality and horizon interpretation in boundary theories.

Abstract

One of the most challenging technical aspects of the dualities between string theory on anti-de Sitter spaces and conformal field theories is understanding how location in the interior of spacetime is represented in the field theory. It has recently been argued that the interior of the spacetime can be directly probed by using intrinsically non-local quantities in the field theory. In addition, Balasubramanian and Ross [hep-th/9906226] argued that when the spacetime described the formation of an AdS_3 black hole, the propagator in the field theory probed the whole spacetime, including the region behind the horizon. We use the same approach to study the propagator for the BTZ black hole and a black hole solution with a single exterior region, and show that it reproduces the propagator associated with the natural vacuum states on these spacetimes. We compare our result with a toy model of the CFT for the single-exterior black hole, finding remarkable agreement. The spacetimes studied in this work are analytic, which makes them quite special. We also discuss the interpretation of this propagator in more general spacetimes, shedding light on certain issues involving causality, black hole horizons, and products of local operators on the boundary.