A defect in holographic interpretations of tensor networks

TL;DR

This paper explores how tensor networks can model non-pure AdS holographic spaces, revealing a defect in current interpretations and proposing new tensor update rules and a novel rayed MERA ansatz.

Contribution

It identifies a defect in existing holographic tensor network models, introduces tensor update mechanisms linked to bulk modes, and proposes the rayed MERA for generalized interface CFTs.

Findings

Tensor updates correspond to non-normalizable bulk modes.

Identified limitations in minimal update theories.

Proposed rayed MERA for specific interface CFTs.

Abstract

We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.