Holographic Tensor Networks in Full AdS/CFT

• DOI: 10.48550/arxiv.1902.10157
• Publication Date: 2019-01-01
• Authors: Bao, Ning; Penington, Geoffrey; Sorce, Jonathan; Wall, Aron C.
• Keywords: High Energy Physics - Theory; Quantum Physics; High Energy Physics - Theory (hep-th); 0103 physical sciences; FOS: Physical sciences; General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph); 01 natural sciences; General Relativity and Quantum Cosmology

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.