Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3

TL;DR

This paper investigates higher spin black holes in AdS3 using Chern-Simons theory, analyzing their asymptotic symmetries, RG flows between fixed points, and thermodynamic properties, revealing complex phase structures and connections to integrable hierarchies.

Contribution

It provides a detailed analysis of asymptotic symmetries and RG flows for higher spin black holes in AdS3, especially for N=4, and explores thermodynamics and phase transitions.

Findings

RG flow from IR W_4 to UV W-symmetry fixed point.

Existence of multiple black hole branches with temperature-dependent stability.

Connection between RG flows and generalized KdV hierarchies.

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.