# Local bulk physics from intersecting modular Hamiltonians

## TL;DR

This paper demonstrates how intersecting modular Hamiltonians in a CFT can be used to construct local bulk operators without prior knowledge of the bulk metric, linking boundary operators to bulk localization.

## Contribution

It introduces a method to derive local bulk operators from boundary CFT data using intersecting modular Hamiltonians, avoiding the need for bulk metric information.

## Key findings

- Constructed local bulk operators from CFT using intersecting modular Hamiltonians.
- Recovered known expressions for bulk observables at zero and finite temperature.
- Established a boundary-to-bulk correspondence based on modular Hamiltonian intersections.

## Abstract

We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces intersect at a point in the bulk then CFT operators which commute with both extended modular Hamiltonians must be localized at the intersection point. We use this to construct local bulk operators purely from CFT considerations, without knowing the bulk metric, using intersecting modular Hamiltonians. For conformal field theories at zero and finite temperature the appropriate modular Hamiltonians are known explicitly and we recover known expressions for local bulk observables.