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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mi>E</mi> </msub> <mfenced close=")" open="("> <mi>A</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{W}}_E(A) $</EquationSource> </InlineEquation> ∪ <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mi>E</mi> </msub> <mfenced close=")" open="("> <mi>B</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{W}}_E(B) $</EquationSource> </InlineEquation> ⊆ <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mi>E</mi> </msub> <mfenced close=")" open="("> <mrow> <mi>A</mi> <mo>∪</mo> <mi>B</mi> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{W}}_E\left(A\cup B\right) $</EquationSource> </InlineEquation>. We demonstrate that already in the simplest example of an AdS3 bulk geometry, EWN can be violated even if A and B are spacelike separated through the bulk and instead we must require the stronger condition that <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mi>E</mi> </msub> <mfenced close=")" open="("> <mi>A</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{W}}_E(A) $</EquationSource> </InlineEquation> be spacelike separated from <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mi>E</mi> </msub> <mfenced close=")" open="("> <mi>B</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{W}}_E(B) $</EquationSource> </InlineEquation>, 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.

Constraints from entanglement wedge nesting for holography at a finite cutoff

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2025年7月9日

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Krishan Saraswat

摘要

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 $W_{E} (A)$ $ {\mathcal{W}}_E(A) $ ∪ $W_{E} (B)$ $ {\mathcal{W}}_E(B) $ ⊆ $W_{E} (A \cup B)$ $ {\mathcal{W}}_E\left(A\cup B\right) $ . We demonstrate that already in the simplest example of an AdS₃ 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 $W_{E} (A)$ $ {\mathcal{W}}_E(A) $ be spacelike separated from $W_{E} (B)$ $ {\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 [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.