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Seeing the Entanglement Wedge

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arxiv 2009.11305 v3 pith:BUJYKQNM submitted 2020-09-23 hep-th

Seeing the Entanglement Wedge

classification hep-th
keywords entanglementwedgeboundarycausalunitarybackreactioncapsclass
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study the problem of revealing the entanglement wedge using simple operations. We ask what operation a semiclassical observer can do to bring the entanglement wedge into causal contact with the boundary, via backreaction. In a generic perturbative class of states, we propose a unitary operation in the causal wedge whose backreaction brings all of the previously causally inaccessible `peninsula' into causal contact with the boundary. This class of cases includes entanglement wedges associated to boundary sub-regions that are unions of disjoint spherical caps, and the protocol works to first order in the size of the peninsula. The unitary is closely related to the so-called Connes Cocycle flow, which is a unitary that is both well-defined in QFT and localised to a sub-region. Our construction requires a generalization of the work by Ceyhan & Faulkner to regions which are unions of disconnected spherical caps. We discuss this generalization in the Appendix. We argue that this cocycle should be thought of as naturally generalizing the non-local coupling introduced in the work of Gao, Jafferis & Wall.

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Cited by 3 Pith papers

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    For the free massless scalar in a Minkowski causal diamond, the vacuum is the unique state or weight in the vacuum sector whose modular flow is local on the null boundary.

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    Modular Witten diagrams reproduce the O(λ² G_N) correction to holographic entanglement entropy, matching the canonical energy term in the quantum Ryu-Takayanagi formula with wedge shape deformation.

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    A semi-classical symplectic two-form is defined as the sum of the gravitational symplectic form and the Berry curvature of the quantum matter state; it is shown to be independent of the Cauchy slice and to satisfy a q...