Local bulk operators in AdS/CFT: a boundary view of horizons and locality

TL;DR

This paper constructs boundary representations of local bulk fields in AdS/CFT, including behind horizons, demonstrating bulk locality and extending to black hole horizons in various AdS geometries.

Contribution

It introduces a boundary operator framework for local bulk fields in AdS, including those behind horizons, maintaining locality and generalizing to higher dimensions.

Findings

Boundary operators have support only at spacelike separated points.

Constructed boundary operators behind horizons that respect bulk locality.

Extended the construction to higher-dimensional AdS black holes.

Abstract

We develop the representation of local bulk fields in AdS by non-local operators on the boundary, working in the semiclassical limit and using AdS_2 as our main example. In global coordinates we show that the boundary operator has support only at points which are spacelike separated from the bulk point. We construct boundary operators that represent local bulk operators inserted behind the horizon of the Poincare patch and inside the Rindler horizon of a two dimensional black hole. We show that these operators respect bulk locality and comment on the generalization of our construction to higher dimensional AdS black holes.