Hawking-Page and entanglement phase transition in 2d CFT on curved backgrounds

TL;DR

This paper investigates the thermodynamics and entanglement properties of 2d CFTs on curved backgrounds, revealing phase transitions similar to Hawking-Page transitions and analyzing their gravity duals.

Contribution

It introduces a method to study 2d CFTs on curved backgrounds via conformal mapping and explores phase transitions and entanglement features in holographic CFTs.

Findings

Hawking-Page like phase transition observed in entanglement entropy

Mutual information analysis reveals correlations in curved spacetime

Gravity duals of 2d CFTs on curved backgrounds discussed

Abstract

The thermodynamics and the entanglement properties of two-dimensional conformal field theories ($2$d CFTs) on curved backgrounds are studied. By means of conformal mapping we study the equivalent system on flat space governed by the deformed Hamiltonian, which is a spatial integral of the Hamiltonian density modulated by an enveloping function. Focusing on holographic CFTs, we observe Hawking-Page like phase transition for the thermal and the entanglement entropy as we vary the background metric. We also compute the mutual information to study the information theoretic correlation between parts of the curved spacetime. The gravity dual of 2d CFTs on curved background is also discussed.