Thermodynamics of higher spin black holes in 3D

Abstract

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) × 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 W3×W3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS3 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(2)3×W(2)3 symmetry deformed by a spin-32 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(2)3×W(2)3 CFT.