Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3

Abstract

We study black holes carrying higher spin charge in AdS3 within the framework of SL(N, R) x SL(N, R) Chern-Simons theory. Focussing attention on the N=4 case, we explicitly analyze the asymptotic symmetry algebra of black hole solutions with a chemical potential for spin-four charge. We demonstrate that the background describes an RG flow between an IR fixed point with W_4 symmetry and a UV fixed point with W-symmetry associated to a non-principal embedding of sl(2) in sl(4). Matching Chern-Simons equations with Ward identities of the deformed CFT, we show that the UV stress tensor is twisted by a certain U(1) current, and the flow is triggered by an operator with dimension 4/3 at the UV fixed point. We find independent confirmation of this picture via a consistent formulation of thermodynamics with respect to this UV fixed point. We further analyze the thermodynamics of multiple branches of black hole solutions for N=4,5 and find that the BTZ-branch, dominant at low temperatures, ceases to exist at higher temperatures following a merger with a thermodynamically unstable branch. We also point out an interesting connection between the RG flows and generalized KdV hierarchies.

References added, version published in Phys. Rev D

References in corpus (4)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Higher Spins in AdS and Twistorial Holography

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• Conformal perturbation theory and higher spin entanglement entropy on the torus
• Brief review on higher spin black holes
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• Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes
• Analysis of higher spin black holes with spin-4 chemical potential
• Phases of higher spin black holes: Hawking-Page, transitions between black holes and a critical point
• On the Explicit Asymptotic ${\mathcal{W}}_5$ Symmetry of 3D Chern-Simons Higher Spin $Ad{S}_3$ Gravity
• Ising Model on Twisted Lattice and Holographic RG flow