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We show that bulk quantities localized on a minimal surface homologous to aboundary region correspond in the CFT to operators that commute with themodular Hamiltonian associated with the boundary region. If two such minimalsurfaces intersect at a point in the bulk then CFT operators which commute withboth 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. Forconformal field theories at zero and finite temperature the appropriate modularHamiltonians are known explicitly and we recover known expressions for localbulk observables.

Local bulk physics from intersecting modular Hamiltonians