Puzzles and pitfalls involving Haar-typicality in holography

TL;DR

This paper discusses the limitations and pitfalls of applying Haar-typicality assumptions to holographic states in AdS/CFT, highlighting potential contradictions and the need for careful interpretation.

Contribution

It identifies specific pitfalls in using Haar-typical states to model holographic states, emphasizing the differences in their properties and implications.

Findings

Haar-typical states do not accurately represent holographic states.

Applying Haar-random ensemble principles can lead to misconceptions.

Holographic states have distinct geometric duals not captured by Haar-typicality.

Abstract

Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.