Constraints from Entanglement Wedge Nesting for Holography at a Finite Cutoff

TL;DR

This paper investigates how entanglement wedge nesting constraints in holography are affected by a finite cutoff, revealing non-local effects and conditions for consistent entanglement structures in AdS/BCFT models.

Contribution

It introduces a new prescription for associating entanglement wedges to subregions on an ETW brane and analyzes the implications for entanglement wedge nesting at finite cutoff.

Findings

EWN can be violated even for spacelike separated regions in simple AdS3 models.

A stronger condition requiring spacelike separation of entanglement wedges is necessary.

Certain RT surfaces connecting the brane to the black hole singularity are disallowed by EWN constraints.

Abstract

We explore constraints that arise from associating an entanglement wedge (EW) to subregions of a cutoff boundary at a finite distance in AdS/CFT, using a subcritical end-of-the-world (ETW) brane acting as a cutoff. In particular, we consider the case of two intervals in the holographic dual to a BCFT, with one interval $A$ located at the asymptotic boundary and the second interval $B$ located on the ETW brane. We discuss in detail subtleties that arise near the RT end-points when defining the EW for this configuration, particularly in the connected phase. Entanglement wedge nesting (EWN) requires that $\mathcal{W}_E(A) \cup \mathcal{W}_E(B) \subseteq \mathcal{W}_E(A\cup B)$. We demonstrate that already in the simplest example of an AdS$_3$ bulk geometry, EWN can be violated even if $A$ and $B$ are spacelike separated through the bulk and instead we must require the stronger condition that $\mathcal{W}_E(A)$ be spacelike separated from $\mathcal{W}_E(B)$, which highlights the non-local nature of the cutoff theory. Our prescription to associate EWs to subregions on the ETW brane is different from the restricted maximin procedure in arXiv:2008.07022 but will agree within the subset of parameter space where EWN is respected. Additionally, we study EWN in a two sided BTZ black hole geometry with an ETW brane in one of the exteriors. In the BTZ black hole example we find that our condition for EWN disallows configurations where the RT surface goes from the brane to the black hole singularity.