Holographic maps from quantum gravity states as tensor networks

TL;DR

This paper constructs bulk/boundary maps in quantum gravity states using tensor networks within the group field theory framework, identifying conditions for holographic behavior based on entanglement structure.

Contribution

It introduces a method to define and analyze bulk/boundary maps for quantum geometric states, establishing criteria for holography in tensor network models of quantum gravity.

Findings

Identified conditions for isometric bulk/boundary maps

Analyzed different quantum states for holographic properties

Connected quantum gravity states with tensor network holography

Abstract

We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms of a partition of the quantum geometric data associated to an open graph into bulk and boundary ones, in the spin representation. We determine the general condition on the entanglement structure of the state that makes the bulk/boundary map isometric (a necessary condition for holographic behaviour), and we analyse different types of quantum states, identifying those that define isometric bulk/boundary maps.