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

TL;DR

This paper resolves a tension in holography by showing that the reduced boundary state is fully characterized when supplemented with an infrared boundary action, derived via a holographic coarse-graining process called rememorization.

Contribution

It introduces holographic rememorization, a Wilsonian coarse-graining method, to define reduced states and partition functions in holography, connecting entanglement wedges with boundary actions.

Findings

Reconciles subregion duality with correlator calculations in the bulk.

Establishes a link between entanglement wedge and IR boundary actions.

Proposes a new coarse-graining procedure called holographic rememorization.

Abstract

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.