How to construct a semi-classical bulk dual for a given CFT state in the context of AdS/CFT correspondence? In particular, I am looking for an explanation/proof of the statement in https://arxiv.org/abs/2502.02633, on page 51:
"In holography, an example of a primary state on the Lorentzian cylinder is the dual of the AdS$_3$ conical defect geometry..."
Similar statements are also made about the vacuum or thermal states of the CFT. These correspond, respectively, to the global AdS and black holes in AdS. Any reference explaining such statements will be useful.
