CFT description of three-dimensional Hawking-Page transition
Yasunari Kurita, Masa-aki Sakagami
TL;DR
This paper models the three-dimensional Hawking-Page transition using conformal field theory, showing how free fermion models can describe the transition as either continuous or first-order depending on modular invariance.
Contribution
It introduces a CFT-based phenomenological model for the Hawking-Page transition, highlighting the role of modular invariance in the nature of the phase transition.
Findings
Free fermion CFT models can describe the Hawking-Page transition.
Modular invariance leads to a continuous transition.
Breaking modular invariance reproduces a first-order transition.
Abstract
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.
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