Revisiting subregion holography using OPE blocks

TL;DR

This paper explores the entanglement wedge representation of AdS3 bulk fields via OPE blocks, revealing their duality conditions and extending the framework to de Sitter space and higher dimensions.

Contribution

It revisits the holographic interpretation of OPE blocks, clarifies their duality to geodesic bulk fields, and extends the analysis to de Sitter space and higher dimensions.

Findings

OPE blocks can be dual to geodesic bulk fields in specific cases.

A combination of Euclidean OPE blocks can represent scalar fields in de Sitter space.

Extended the analysis to simple higher-dimensional examples.

Abstract

In this short note, we revisit the entanglement wedge representation of AdS$_3$ bulk fields in terms of CFT operator product expansion (OPE) blocks for a general class of blocks. Given a boundary interval and its associated causal diamond, the OPEs involve boundary operators with or without spin, and located either at spacelike or timelike edges of the diamond. Only for a subset of these cases, can the OPE block be dual to a geodesic bulk field. We show that when applied to de Sitter, a suitable combination of Euclidean OPE blocks can represent a dS scalar integrated over the timelike extremal surfaces, which play an important role in defining pseudo-entropy. We also work out some simple higher dimensional examples.