Subregion duality, wedge classification and no global symmetries in AdS/CFT

TL;DR

This paper explores various notions of subregion duality in AdS/CFT, clarifies differences between background and operator reconstruction wedges, and strengthens the proof against global symmetries in geometrical states.

Contribution

It distinguishes four types of operator reconstruction wedges and resolves paradoxes related to subregion duality, advancing understanding of holographic dualities.

Findings

Clarified differences between background and operator reconstruction wedges

Resolved paradox in subregion duality context

Enhanced proof of absence of global symmetries in geometrical states

Abstract

We study various notions of `subregion duality' in the context of AdS/CFT. We highlight the differences between the `background wedge' and the `operator reconstruction wedges,' providing a resolution to the paradox raised in \cite{Bao:2019hwq}. Additionally, we elucidate the distinctions between four different `operator reconstruction wedges' and demonstrate how to enhance the proof for the absence of global symmetries in geometrical states in AdS/CFT \cite{Harlow:2018jwu, Harlow:2018tng} as an example of these distinctions.