Emergent geometry, thermal CFT and surface/state correspondence

TL;DR

This paper explores a conjectured surface/state duality linking convex surfaces to quantum states, demonstrating how thermal geometries like BTZ black holes emerge from boundary CFT entanglement using a generalized tensor network approach.

Contribution

It generalizes the thermofield double formalism to continuum multi-scale entanglement renormalization and proposes a framework connecting boundary CFTs to emergent thermal geometries.

Findings

Thermal geometries emerge from boundary CFT entanglement.

Information metric calculations yield BTZ black hole or thermal AdS.

Framework applies to 2D CFTs at finite temperature.

Abstract

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.