2013/06/30 by Alexandre Belin, Alexander Maloney, Shunji Matsuura
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Dimension (graph theory) #Entropy (arrow of time) #Geometry #Horizon #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Phase transition #Physics #Principle of maximum entropy #Quantum many-body systems #Quantum mechanics #Rényi entropy #Scalar (mathematics) #Scalar field #Statistics #cond-mat.str-el #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep12(2013)050
21 pages, 7 figures, v3 - References added. Neumann boundary conditions added in section 5
openalex publication_date 2013/12/01 · arxiv created 2015/01/20 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider Renyi entropies of conformal field theories in flat space, with the entangling surface being a sphere. The AdS/CFT correspondence relates this Renyi entropy to that of a black hole with hyperbolic horizon; as the Renyi parameter n increases the temperature of the black hole decreases. If the CFT possesses a sufficiently low dimension scalar operator the black hole will be unstable to the development of hair. Thus, as n is varied, the Renyi entropies will exhibit a phase transition at a critical value of n. The location of the phase transition, along with the spectrum of the reduced density matrix ρ, depends on the dimension of the lowest dimension non-trivial scalar operator in the theory.