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There is some tension between two well-known ideas in holography. On the onehand, subregion duality asserts that the reduced density matrix associated witha limited region of the boundary theory is dual to a correspondingly limitedregion in the bulk, known as the entanglement wedge. On the other hand,correlators that in the boundary theory can be computed solely with thatdensity matrix are calculated in the bulk via the GKPW or BDHM prescriptions,which require input from beyond the entanglement wedge. We show that thistension is resolved by recognizing that the reduced state is only fullyidentified when the entanglement wedge is supplemented with a specific infraredboundary action, associated with an end-of-the-world brane. This action isobtained by coarse-graining through a variant of Wilsonian integration, aprocedure that we call holographic rememorization, which can also be applied todefine other reduced density or transition matrices, as well as more generalreduced partition functions. We find an interesting connection with AdS/BCFT,and, in this context, we are led to a simple example of an equivalence betweenan ensemble of theories and a single theory, as discussed in recent studies ofthe black hole information problem.

Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries