A CFT Perspective on Gravitational Dressing and Bulk Locality

TL;DR

This paper explores how gravitational dressing affects bulk locality in AdS/CFT, using 2+1D models, cross-cap states, and conformal symmetry to understand the construction of local bulk operators.

Contribution

It provides explicit correlation functions, links the HKLL recipe to CFT crossing conditions, and demonstrates how Virasoro symmetry and bootstrap principles underpin bulk locality.

Findings

Correlation functions free of non-local branch cuts

Recovery of bulk locality via CFT crossing conditions

Cross-cap states solve bulk wave equations in certain gauges

Abstract

We revisit the construction of local bulk operators in AdS/CFT with special focus on gravitational dressing and its consequences for bulk locality. Specializing to 2+1-dimensions, we investigate these issues via the proposed identification between bulk operators and cross-cap boundary states. We obtain explicit expressions for correlation functions of bulk fields with boundary stress tensor insertions, and find that they are free of non-local branch cuts but do have non-local poles. We recover the HKLL recipe for restoring bulk locality for interacting fields as the outcome of a natural CFT crossing condition. We show that, in a suitable gauge, the cross-cap states solve the bulk wave equation for general background geometries, and satisfy a conformal Ward identity analogous to a soft graviton theorem, Virasoro symmetry, the large N conformal bootstrap and the uniformization theorem all play a key role in our derivations.