Which quantum states are dual to classical spacetimes?

TL;DR

This paper identifies the specific conformal field theory states that correspond to classical spacetimes in the holographic duality, showing they are related to coherent states and linearized perturbations, with implications for black hole states and spacetime emergence.

Contribution

It provides a prescription for selecting CFT states dual to classical spacetimes and links them to coherent states, enhancing understanding of holographic correspondence and spacetime emergence.

Findings

CFT states dual to classical spacetimes are coherent states or linearized perturbations.

Black hole dual states are superpositions of these coherent states.

Implications for the quantum nature of spacetime and phase transitions like Hawking-Page.

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.