Holographic Tensor Networks in Full AdS/CFT

TL;DR

This paper introduces a method to construct tensor networks that encode the geometry of bulk spacetime in AdS/CFT, capturing sub-AdS scale structures using holographic entanglement principles.

Contribution

It provides a general procedure for building tensor networks representing geometric states in AdS/CFT, linking boundary states to bulk geometries at various scales.

Findings

Tensor networks can encode bulk spacetime geometry.

The method captures sub-AdS scale structures.

It connects entanglement properties to geometric features.

Abstract

We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual, our procedure produces a tensor network for the boundary state whose internal geometry matches (a discretization of) the bulk spacetime geometry. By invoking the "holographic entanglement of purification" conjecture, our construction can be made to capture the structure of the bulk spacetime at sub-AdS scales.