Which quantum states are dual to classical spacetimes?

Abstract: It is commonly accepted that states in a conformal field theory correspond to classical spacetimes with Anti-de-Sitter asymptotics. In this work we give a prescription for the CFT states with a dual classical spacetime and, using basic holographic rules, show that they are holographically connected to coherent states in the large-N limit, or by considering linearized perturbations. We also point out implications in the spacetime emergence mechanism, for instance, the (entangled) state dual to the black hole should be properly described as a quantum superposition of products of these states. This also complements the quantum interpretation of the Hawking-Page transition.