Thermodynamics of higher spin black holes in 3D

TL;DR

This paper explores the thermodynamics of higher spin black holes in 3D Chern-Simons theory, revealing multiple solution branches, flow between different AdS_3 backgrounds, and the role of W_3 symmetries in their thermodynamic behavior.

Contribution

It provides a detailed analysis of black hole solutions with spin-3 charges, identifying their thermodynamic phases and the dual CFT descriptions involving W_3 symmetries.

Findings

Multiple solution branches describe flows between AdS_3 backgrounds.

High temperature behavior is dominated by a W_3^(2) x W_3^(2) CFT.

Thermodynamics aligns with Ward identities of deformed W_3 CFT.

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.