Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes

Abstract

Motivated by the understanding of holography as realized in tensor networks, we develop a bulk procedure that can be interpreted as generating a sequence of coarse-grained holographic states. The coarse-graining procedure involves identifying degrees of freedom entangled at short distances and disentangling them. This is manifested in the bulk by a flow equation that generates a codimension-1 object, which we refer to as the holographic slice. We generalize the earlier classical construction to include bulk quantum corrections, which naturally involves the generalized entropy as a measure of the number of relevant boundary degrees of freedom. The semiclassical coarse-graining results in a flow that approaches quantum extremal surfaces such as entanglement islands that have appeared in discussions of the black hole information paradox. We also discuss the relation of the present picture to the view that the holographic dictionary works as quantum error correction.

16 pages, 14 figures, typos corrected

References in corpus (7)

• Causality & holographic entanglement entropy
• A holographic proof of the strong subadditivity of entanglement entropy
• Surface/State Correspondence as a Generalized Holography
• Islands in Asymptotically Flat 2D Gravity
• Sphere partition functions and cut-off AdS
• Comments on Holographic Entanglement Entropy in TT Deformed CFTs
• Holographic Tensor Networks in Full AdS/CFT

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• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds