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

Abstract: We study various notions of subregion duality' in the context of AdS/CFT. We highlight the differences between thebackground wedge' and the operator reconstruction wedges,' providing a resolution to the paradox raised in \cite{Bao:2019hwq}. Additionally, we elucidate the distinctions between four differentoperator 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.