A modular toolkit for bulk reconstruction

TL;DR

This paper develops new modular tools in AdS/CFT to analyze bulk causality and locality, enabling direct extraction of the RT surface and connecting to the Quantum Null Energy Condition.

Contribution

It introduces a modular toolkit that links boundary entanglement properties to bulk geometric features, including a conjectured set of rules for geodesic-RT surface interactions.

Findings

Relation between modular analyticity and entanglement wedge nesting

Method to locate RT surface from boundary data

Connection to Quantum Null Energy Condition

Abstract

We introduce new tools for studying modular flow in AdS/CFT. These tools allow us to efficiently extract bulk information related to causality and locality. For example, we discuss the relation between analyticity in modular time and entanglement wedge nesting which can then be used to extract the location of the Ryu-Takayanagi (RT) surface directly from the boundary theory. Probing the RT surface close to the boundary our results reduce to the recent proof of the Quantum Null Energy Condition. We focus on heavy probe operators whose correlation functions are determined by spacelike geodesics. These geodesics interplay with the RT surface via a set of rules that we conjecture and give evidence for using the replica trick.