Thermal geometry from CFT at finite temperature

TL;DR

This paper explores how thermal geometries like BTZ black holes and thermal AdS emerge from 2D conformal field theories at finite temperature using the cMERA entanglement renormalization network, and proposes a cMERA-based description of the Hawking-Page phase transition.

Contribution

It introduces a cMERA framework to derive thermal geometries from CFT and models the Hawking-Page transition within this approach, linking it to the surface/state correspondence.

Findings

Thermal geometries correspond to reduced states in 2D CFTs.

The cMERA approach reproduces BTZ and thermal AdS geometries.

A cMERA-based model of the Hawking-Page transition is proposed.

Abstract

We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of $2d$ CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking-Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.