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arXiv:2501.15024 · Journal of High Energy Physics

Constraints from entanglement wedge nesting for holography at a finite cutoff

Krishan Saraswat

Published Jul 9, 2025• 0 citations
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Abstract

A bstract 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 $$ {\mathcal{W}}_E(A) $$ W E A ∪ $$ {\mathcal{W}}_E(B) $$ W E B ⊆ $$ {\mathcal{W}}_E\left(A\cup B\right) $$ W E A ∪ 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 $$ {\mathcal{W}}_E(A) $$ W E A be spacelike separated from $$ {\mathcal{W}}_E(B) $$ 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 [1] 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.

DOI
10.1007/jhep07(2025)120

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A bstract 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 WE(A){\mathcal{W}}_E(A)WE​(A) W E A ∪ WE(B){\mathcal{W}}_E(B)WE​(B) W E B ⊆ WE(A∪B){\mathcal{W}}_E\left(A\cup B\right)WE​(A∪B) W E A ∪ 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 WE(A){\mathcal{W}}_E(A)WE​(A) W E A be spacelike separated from WE(B){\mathcal{W}}_E(B)WE​(B) 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 [1] 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.
A bstract In the AdS/CFT correspondence, the causal structure of the bulk AdS spacetime is tied to entanglement in the dual CFT. This relationship is captured by the connected wedge theorem [1], which states that a bulk scattering process implies the existence of O (1/ G N ) entanglement between associated boundary subregions. In this paper, we study the connected wedge theorem in two asymptotically AdS 2+1 spacetimes: the conical defect and BTZ black hole geometries. In these settings, we find that bulk scattering processes require not just large entanglement, but also additional restrictions related to candidate RT surfaces which are non-minimal. We argue these extra relationships imply a certain CFT entanglement structure involving internal degrees of freedom. Because bulk scattering relies on sub-AdS scale physics, this supports the idea that sub-AdS scale locality emerges from internal degrees of freedom. While the new restriction that we identify on non-minimal surfaces is stronger than the initial statement of the connected wedge theorem, we find that it is necessary but still not sufficient to imply bulk scattering in mixed states.
A bstract Recently it was proposed that, the AdS/BCFT correspondence can be simulated by a holographic Weyl transformed CFT 2 , where the cut-off brane plays the role of the Karch-Randall (KR) brane [1]. In this paper, we focus on the Weyl transformation that optimizes the path integral computation of the reduced density matrix for a single interval in a holographic CFT 2 . When we take the limit that one of the endpoint of the interval goes to infinity (a half line), such a holographic Weyl transformed CFT 2 matches the AdS/BCFT configuration for a BCFT with one boundary. Without taking the limit, the induced cutoff brane becomes a circle passing through the two endpoints of the interval. We assume that the cutoff brane also plays the same role as the KR brane in AdS/BCFT, hence the path-integral-optimized purification for the interval is in the island phase. This explains the appearance of negative mutual information observed in [2]. We check that, the entanglement entropy and the balanced partial entanglement entropy (BPE) calculated via the island formulas, exactly match with the RT formula and the entanglement wedge cross-section (EWCS), which are allowed to anchor on the cutoff brane.
Abstract: \nTensor networks,ToverlineT T\\overline{T} ToverlineTTT¯, and broader notions of a holographic principle all motivate the idea that some notion of gravitational holography should persist in the presence of a radial cutoff. But in the absence of time-reflection symmetry, the areas of Hubeny-Rangamani-Takayanagi surfaces anchored to the radial cutoff generally violate strong sub-additivity, even when the associated boundary regions are spacelike separated as defined by both bulk and boundary notions of causality. We thus propose an alternate definition of cutoff-holographic entropy using a restricted maximin prescription anchored to a codimension 2 cutoff surface. For bulk solutions that respect the null energy condition, we show that the resulting areas satisfy SSA, entanglement wedge nesting, and monogamy of mutual information in parallel with cutoff free results in AdS. These results hold even when the cutoff surface fails to be convex.
In this work we consider a particular codimension-1 region of a holographic spacetime which we call the entanglement wedge polygon (EWP). For a pure state and a partition of the boundary into a number of regions AiA_iAi​ the EWP is defined as the region external to all the individual homology regions rAir_{A_i}rAi​​ which consists of the intersection of the entanglement wedge EW(AiA_iAi​) with the time slice. In vacuum AdS3_33​ and BTZ spacetime, the quantity is topological as a direct consequence of the Gauss-Bonnet theorem. In higher dimensions we make progress by considering a number of concrete examples including vacuum, black brane, and soliton solutions of AdSd+1_{d+1}d+1​ as well as spacetime geometries with end of the world branes dual to boundary conformal field theories. We provide a suitable generalization to mixed states and comment on possible connections between the EWP and measures of multi-partite entanglement.
Abstract Recently, it was proposed that a TT‾ T\overline{T} TT T T ¯ deformed CFT is dual to a gravity theory in an asymptotically AdS spacetime at finite radial cutoff. Motivated by this proposal, we explore some aspects of Hyperscaling Violating geometries at finite cutoff and zero temperature. We study holographic entanglement entropy, mutual information (HMI) and entanglement wedge cross section (EWCS) for entangling regions in the shape of strips. It is observed that the HMI shows interesting features in comparison to the very small cutoff case: it is a decreasing function of the cutoff. It is finite when the distance between the two entangling regions goes to zero. The location of its phase transition also depends on the cutoff, and decreases by increasing the cutoff. On the other hand, the EWCS is a decreasing function of the cutoff. It does not show a discontinuous phase transition when the HMI undergoes a first-order phase transition. However, its concavity changes. Moreover, it is finite when the distance between the two strips goes to zero. Furthermore, it satisfies the bound EW ≥ I2 \frac{I}{2} 2I​ I 2 for all values of the cutoff.
The entanglement wedge cross section in holographic picture provides a geometrical description of the entanglement for mixed states. In this paper we study the inequalities for the entanglement wedge cross section in AdS/BCFT duality. In the presence of the boundary in conformal field theory (CFT), the dual entanglement wedge cross section exhibits abundant phase structures since the extremal surface may end on the brane. We present a universal treatment which is applicable for all the possible phases such that the inequalities for the entanglement wedge cross section can be proved in an algebraic manner rather than a diagrammatic manner. We show that the entanglement wedge cross section in AdS/BCFT satisfies the same inequalities as in AdS/CFT.