The CFT-interpolating Black Hole in Three Dimensions

Abstract

We present a new exact black hole solution in three dimensional Einstein gravity coupled to a single scalar field. This is one of the extended solutions of the BTZ black hole and has in fact ${\text{AdS}}_3$ geometries both at the spatial infinity and at the event horizon. An explicit derivation of Virasoro algebras for ${\text{CFT}}_2$ at the two boundaries is shown to be possible à la Brown and Henneaux's calculation. If we regard the scalar field as a running coupling in the dual two dimensional field theory, and its flow in the bulk as the "holographic" renormalization group flow, our black hole should interpolate the two ${\text{CFT}}_2$ living at the infinity and at the horizon. Following the Hamilton-Jacobi analysis by de Boer, Verlinde and Verlinde, we calculate the central charges $c_{\text{UV}}$ and $c_{\text{IR}}$ for the ${\text{CFT}}_2$ on the infinity and the horizon, respectively. We also confirm that the inequality $c_{\text{IR}}<c_{\text{UV}}$ is satisfied, which is consistent with the Zamolodchikov's c-theorem.

20 pages, 2 figures, references added

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• The RN/CFT Correspondence
• Hawking-Page phase transition in BTZ black hole revisited
• Hidden Conformal Symmetry of the Kerr-Newman Black Hole
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• Extremal Isolated Horizon/CFT Correspondence
• Hidden conformal symmetry of rotating charged black holes
• On Holographic Dual of the Dyonic Reissner-Nordström Black Hole
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• Extremal Kerr/CFT correspondence of five-dimensional rotating (charged) black holes with squashed horizons
• Yet Another Realization of Kerr/CFT Correspondence
• Hidden Conformal Symmetry of the Reissner-Nordstrøm Black Holes
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• Conformal Symmetry for Rotating D-branes
• Hidden conformal symmetry of extreme and non-extreme Einstein-Maxwell-Dilaton-Axion black holes
• Quasi-local conserved charges and holography
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• Holographic Duals of Near-extremal Reissner-Nordstrom Black Holes
• A New Spin on the Weak Gravity Conjecture
• Black Hole Vacua and Rotation
• Zeta(n) via hyperbolic functions
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• New Near Horizon Limit in Kerr/CFT
• BPS-like bound and thermodynamics of the charged BTZ black hole
• The a-theorem and conformal symmetry breaking in holographic RG flows
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• Gravity duals for logarithmic conformal field theories
• The RN/CFT Correspondence Revisited
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• Holographic Symmetry-Breaking Phases in AdS${}_3$/CFT${}_2$
• Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity
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• Extremal Black Holes and Holographic C-Theorem
• Canonical energy and hairy AdS black holes
• Scalar hairs and exact vortex solutions in 3D AdS gravity
• Ising Model on Twisted Lattice and Holographic RG flow