Emergence of Spacetime from the Algebra of Modular Hamiltonians

Modular flow, generated by a modular Hamiltonian, is an operation in quantum field theory that preserves a given subregion. In a holographic setting modular flow on the boundary preserves a dual subregion of the bulk space-time. Modular flow leaves the boundary of this subregion fixed, thus a point in the bulk corresponds to a family of modular Hamiltonians whose fixed surfaces all intersect at the bulk point. This family defines a maximal subalgebra within the algebra Η generated by all modular Hamiltonians. This suggests an algebraic approach to bulk reconstruction, in the spirit of non-commutative geometry: the bulk spacetime can be recovered as the space of maximal subalgebras of Η.