Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy

Abstract

We extend the charged Renyi entropy to a more general holographic scenario. Coupling an arbitrary non-linear electrodynamics Lagrangian density to AdS gravity, we analyse the thermodynamic features of non-linearly charged hyperbolic black holes and the thermal fluctuations in the grand canonical ensemble. We provide a general form for the relevant holographic quantities that describes a CFT with a global $U(1)$ symmetry in terms of horizon data and we compute the first thermal fluctuation of the charged Renyi entropy. We demonstrate the validity of the formulae through an analytic example; the Coulomb source in $2+1$ dimensions. We propose this model to be dual to charged free bosons in $1+1$ dimensions. The corrections generates a subleading logarithmic divergence in the entanglement entropy which appear in some Condensed Matter systems with spontaneous symmetry breaking due to IR effects in the ground state. We comment on the possibility of interpreting these results in terms of holography beyond the saddle point approximation.

41 pages, 6 figures. Comments are welcome. V2: minor corrections, references added. V3: Matches accepted version in JHEP

References in corpus (23)

• Towards a derivation of holographic entanglement entropy
• Seeing a c-theorem with holography
• Higher-dimensional black holes with a conformally invariant Maxwell source
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Universality of corner entanglement in conformal field theories
• Introductory Notes on Non-linear Electrodynamics and its Applications
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
• Thermodynamics of higher dimensional black holes with higher order thermal fluctuations
• Hawking-Page phase transition in BTZ black hole revisited
• Fake Supersymmetry and Extremal Black Holes
• Logarithmic correction to black hole entropy from the nonlocality of quantum gravity
• A Smarr formula for charged black holes in nonlinear electrodynamics
• Holographic entanglement density for spontaneous symmetry breaking
• Charged Rényi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals
• Higher-derivative holography with a chemical potential
• Logarithmic Corrections, Entanglement Entropy, and UV Cutoffs in de Sitter Spacetime
• A universal feature of charged entanglement entropy
• Logarithmic corrections to the entropy function of black holes in the open ensemble
• Quantum Thermodynamics of a Quantum Sized AdS Black Hole
• Instability of Universal Terms in the Entanglement Entropy
• Interpolating Boundary Conditions on $Ad{S}_2$
• Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order

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• Thermal fluctuations of (non)linearly charged BTZ black hole in massive gravity
• Three-dimensional accelerating AdS black holes in $F(R)$ gravity
• On regular charged black holes in three dimensions
• Thermodynamics of deformed AdS-Schwarzschild black holes in the presence of Thermal fluctuations
• Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair