Holographic phases of Rényi entropies

Abstract

We consider Rényi entropies S n = 1 1−n log Tr ρ n of conformal field theories in flat space, with the entangling surface being a sphere. The AdS/CFT correspondence relates this Rényi entropy to that of a black hole with hyperbolic horizon; as the Rényi 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 Rényi 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.

Cosmological model from the holographic equipartition law with a modified Rényi entropy

“…Nonextensive entropies for black-hole thermodynamics have been extensively investigated [91,112,113,[122][123][124][125][126]. Recently, Biró and Czinner [112] suggested a novel type of Rényi entropy on black-hole horizons, by regarding the Bekenstein-Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula.…”

Anomalies and entanglement entropy

“…The analytic continuation from integer n ≥ 2 to n = 1 used in (1.2a) is usually carried out under an implicit assumption regarding a replica symmetry, Z n , between sheets in M n . See e.g., the discussions in [34][35][36] for the role of the Z n symmetry in the holographic formula of entanglement entropy [37,38]. In the remainder of this work we will assume that the analytic continuation from non-integer n to integer n can be carried out and take (1.2a) to be the definition of the entanglement entropy in quantum field theory.…”

Non-analyticity of holographic Rényi entropy in Lovelock gravity

“…The novelty here is to take into account that such black holes undergo phase transitions, to systematically span the causal parameter space, and analyse the consequences for the dual RE. Connections between RE and bulk phase transitions have been previously studied in [46,47]. However, there are two main differences here.…”

“…First of all, our system is purely gravitational, dual to a CFT in its vacuum state with the only corrections coming from the corrections of the coupling constants. In [46] the authors holographically computed RE by considering Einstein gravity with the addition of a scalar field (similarly in [47] for the case of a charged system), and the instability of hyperbolic black holes is due to the development of hair. Second, our phase transition is first order, while in [46,47] it is second order.…”

“…In [46] the authors holographically computed RE by considering Einstein gravity with the addition of a scalar field (similarly in [47] for the case of a charged system), and the instability of hyperbolic black holes is due to the development of hair. Second, our phase transition is first order, while in [46,47] it is second order. This has a crucial effect on the RE: our results show that for strongly coupled dual CFT's the RE displays a kink at a critical index n which results in the non-analyticity of RE with respect to n nearby the kink.…”