Pulling the Boundary into the Bulk

TL;DR

The paper introduces the holographic slice, a covariant bulk object that models coarse-grained holographic states, linking entanglement, geometry, and tensor networks in a novel way.

Contribution

It presents the holographic slice as a new covariant bulk construct that captures coarse-graining and entanglement features in holography, with properties supporting its boundary interpretation.

Findings

Holographic slice exhibits monotonic area and entanglement entropy.

It cannot probe beyond late-time black hole horizons.

The slice can traverse entanglement shadows.

Abstract

Motivated by the ability to consistently apply the Ryu-Takayanagi prescription for general convex surfaces and the relationship between entanglement and geometry in tensor networks, we introduce a novel, covariant bulk object - the holographic slice. The holographic slice is found by considering the continual removal of short range information in a boundary state. It thus provides a natural interpretation as the bulk dual of a series of coarse-grained holographic states. The slice possesses many desirable properties that provide consistency checks for its boundary interpretation. These include monotonicity of both area and entanglement entropy, uniqueness, and the inability to probe beyond late-time black hole horizons. Additionally, the holographic slice illuminates physics behind entanglement shadows, as minimal area extremal surfaces anchored to a coarse-grained boundary may probe entanglement shadows. This lets the slice flow through shadows. To aid in developing intuition for these slices, many explicit examples of holographic slices are investigated. Finally, the relationship to tensor networks and renormalization (particularly in AdS/CFT) is discussed.