Bulk locality from modular flow

Understand

We study the reconstruction of bulk operators in the entanglement wedge in terms of low energy operators localized in the respective boundary region.

• To leading order in $N$, the dual boundary operators are constructed from the modular flow of single trace operators in the boundary subregion.
• The appearance of modular evolved boundary operators can be understood due to the equality between bulk and boundary modular flows and explicit formulas for bulk operators can be found with a complete understanding of the action of bulk modular flow, a difficult but in principle solvable task.
• We also obtain an expression when the bulk operator is located on the Ryu-Takayanagi surface which only depends on the bulk to boundary correlator and does not require the explicit use of bulk modular flow.