Emergent geometry, thermal CFT and surface/state correspondence.

We study a conjectured correspondence between any codimension-two convex surface and a quantum state (SS-duality for short). By applying thermofield double formalism to the SS-duality, we show that thermal geometries naturally emerge as a result of hidden quantum entanglement between two boundary CFTs. We therefore propose a general framework to emerge the thermal geometry from CFT at finite temperature, without knowing many details about the thermal CFT. As an example, the case of 2 d CFT is considered. We calculate its information metric and show that it is either BTZ black hole or thermal AdS as expected. [ABSTRACT FROM AUTHOR]