Holographic representation of local bulk operators

TL;DR

This paper constructs explicit CFT operators dual to local bulk fields in AdS/CFT, demonstrating how boundary operators encode bulk locality and saturate holographic bounds at finite N.

Contribution

It provides a general method to explicitly construct boundary operators corresponding to local bulk fields in various coordinate systems.

Findings

CFT operators can have compact support in a complexified boundary region.

At finite N, the number of independent operators within a bulk volume saturates the holographic bound.

The construction applies to general dimensions and multiple coordinate systems.

Abstract

The Lorentzian AdS/CFT correspondence implies a map between local operators in supergravity and non-local operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical limit. The computation is done for general dimension in global, Poincare and Rindler coordinates. We find that the CFT operators can be taken to have compact support in a region of the complexified boundary whose size is set by the bulk radial position. We show that at finite N the number of independent commuting operators localized within a bulk volume saturates the holographic bound.