In holographic duality a higher dimensional quantum gravity system emerges from a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom, N. Bulk geometric notions such as spacetime subregions, extremal surfaces, and causal structure are only sharply defined in the bulk G_N to 0 limit which corresponds to the boundary N to infty limit. In this talk, we will argue that geometric notions in the bulk emerge from the mathematical structure of the large N limit of the dual CFT, which we have shown gives rise to the ubiquitous emergence of type III_1 von Neumann algebras. We explicitly construct the boundary subalgebras that describe bulk physics in most bulk subregions. We also comment on the relationship of our construction with quantum error correction, subregion-subregion duality and the RT prescription.

MIT