CFT description of the three-dimensional Hawking-Page transition

We construct a phenomenological conformal field theory (CFT) model of the three-dimensional Hawking-Page transition. We find that free fermion CFT models on the boundary torus give a description of the three-dimensional Hawking-Page transition. If modular invariance is respected, the free fermion model implies that the transition occurs continuously through the conical space phase and the small black hole phase. On the other hand, if we are allowed to break modular invariance, we can construct a free fermion model that reproduces the usual Euclidean semi-classical result, and in particular exhibits a first-order phase transition.