Background independent tensor networks

TL;DR

This paper introduces a background independent tensor network model for holographic maps, enabling the representation of larger code subspaces without fixed background entanglement, thus better mimicking dynamical gravity.

Contribution

It demonstrates that tensor networks can be constructed without background entanglement, expanding their applicability to more dynamic holographic models.

Findings

Background independent tensor networks are feasible.

They allow modeling of larger holographic code subspaces.

Connection to recent random CFT data discussions.

Abstract

Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ``background entanglement'', i.e. links of a fixed state, often the maximally entangled state. However, these constructions fall short of modeling real holographic maps. One reason is that their ``areas'' are trivial, taking the same value for all states, unlike in gravity where the geometry is dynamical. Recently, new constructions have ameliorated this issue by adding degrees of freedom that ``live on the links''. This makes areas non-trivial, equal to the background entanglement piece plus a new positive piece that depends on the state of the link degrees of freedom. Nevertheless, this still has the downside that there is background entanglement, and hence it only models relatively limited code subspaces in which every area has a definite minimum value given by the background entanglement. In this note, we simply point out that a version of these constructions goes one step further: they can be background independent, with no background entanglement in the holographic map. This is advantageous because it allows tensor networks to model holographic maps for larger code subspaces. In addition to pointing this out, we address some subtleties involved in making it work and point out a nice connection it offers to recent discussions of random CFT data.