  We study a conjectured correspondence between any codimension two convex
surface and a quantum state (SS-duality for short). By generalizing thermofield
double formalism to continuum version of the multi-scale entanglement
renormalization ansatz (cMERA) and using the SS-duality, we show that thermal
geometries naturally emerge as a result of hidden quantum entanglement between
boundary CFTs. We therefore propose a general framework to emerge the thermal
geometry from CFT at finite temperature. As an example, the case of $2d$ CFT is
considered. We calculate its information metric and show that it is either BTZ
black hole or thermal AdS as expected.
