CFT description of three-dimensional Hawking-Page phase transition

After a brief review of three-dimensional gravity with Λ < 0 and of the Hawking-Page phase transition, we consider the three-dimensional transition in terms of the boundary conformal field theory(CFT). We find that the free fermions CFT on the boundary torus has a good description for it. Around the critical temperature where semi-classical approximation does not work, the free fermions model predicts that the transition will smoothly occur through the conical space and a small black hole phase. In classical limit, the most dominant contribution there comes only from the NS-NS sector in free fermions CFT on the boundary torus. We also find that the properties of the semiclassical result can be obtained by neglecting the NS-NS sector and considering only two NS-R and R-NS sectors.