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