Constructing local bulk observables in interacting AdS/CFT

TL;DR

The paper tackles the challenge of defining local bulk observables in interacting AdS/CFT beyond leading order in $1/N$. It develops a CFT-based construction that preserves bulk locality by correcting the naive smeared bulk operators with higher-dimension primaries and, in some approaches, bilocal terms, leveraging large-$N$ factorization. The authors show that unwanted logarithmic singularities and bulk nonlocalities can be canceled order-by-order, first in AdS$_2$ and then in AdS$_3$, and connect these corrections to bulk perturbation theory and Feynman diagrams. The work provides a concrete perturbative framework for emergent bulk locality in holography, while clarifying how locality may break down nonperturbatively at finite $N$ and suggesting implications for quantum gravity.

Abstract

Local operators in the bulk of AdS can be represented as smeared operators in the dual CFT. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. Large-N factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.