Abstract
We analytically study phase transitions of holographic charged Rényi entropies in two gravitational systems dual to the mathcal{N} = 4 super-Yang-Mills theory at finite density and zero temperature. The first system is the Reissner-Nordström-AdS5 black hole, which has finite entropy at zero temperature. The second system is a charged dilatonic black hole in AdS5, which has zero entropy at zero temperature. Hyperbolic black holes are employed to calculate the Rényi entropies with the entangling surface being a sphere. We perturb each system by a charged scalar field, and look for a zero mode signaling the instability of the extremal hyperbolic black hole. Zero modes as well as the leading order of the full retarded Green’s function are analytically solved for both systems, in contrast to previous studies in which only the IR (near horizon) instability was analytically treated.
Highlights
We perturb each system by a charged scalar field, and look for a zero mode signaling the instability of the extremal hyperbolic black hole
We review the relation between Rényi entropies and hyperbolic black holes very briefly, but it is sufficient for the purpose of this paper
We have analytically solved the zero modes triggering the instability in two systems of charged hyperbolic black holes at zero temperature
Summary
We review the relation between Rényi entropies and hyperbolic black holes very briefly, but it is sufficient for the purpose of this paper. Phase transitions of Rényi entropies with the entangling surface being a sphere are studied in terms of hyperbolic black holes. The reduced density matrix for the subsystem A is ρA = TrBρ. The charged Rényi entropy is defined by [6]. Where μ is the entanglement chemical potential, and QA measures the amount of charge in the subsystem A, and NA(μ) ≡ Tr[ρAeμQA] is a normalization factor. Suppose we want to calculate the Rényi entropies of a CFT with a gravity dual, and the entangling surface is a sphere of radius R. The Rényi entropy is related to the free energy of a hyperbolic black hole: Sn(μ).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
