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arXiv · 1210.0284

Thermodynamics of higher spin black holes in 3D

Justin R. David·Michael Ferlaino·S. Prem Kumar
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Abstract

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3,R) x SL(3,R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W_3 x W_3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS_3 backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W_3^(2) x W_3^(2) symmetry deformed by a spin-3/2 current. This allows to identify the precise map between UV and IR thermodynamic variables. We find that the high temperature regime is dominated by a black hole branch whose thermodynamics can only be consistently inferred with reference to this W_3^(2) x W_3^(2) CFT.

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Justin R. David, Michael Ferlaino, S. Prem Kumar. 2012-10-01. Thermodynamics of higher spin black holes in 3D. https://doi.org/10.1007/jhep11(2012)135

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