About the phase space of SL(3) Black Holes

TL;DR

This paper investigates the phase space structure and asymptotic symmetry algebra of higher spin black holes in SL(3) Chern-Simons theory, revealing an isomorphism to a specific W-algebra in perturbation.

Contribution

It computes the Dirac bracket algebra for two phase spaces of SL(3) higher spin black holes, demonstrating an explicit isomorphism to W^{(2)}_3 imes W^{(2)}_3.

Findings

Derived the fixed time Dirac bracket algebra for the phase spaces.

Showed the algebra is isomorphic to W^{(2)}_3 imes W^{(2)}_3 in perturbation.

Analyzed the asymptotic symmetry algebra of higher spin black holes.

Abstract

In this note we address some issues of recent interest, related to the asymptotic symmetry algebra of higher spin black holes in $sl(3,\mathbb{R})\times sl(3,\mathbb{R})$ Chern Simons (CS) formulation. We compute the fixed time Dirac bracket algebra that acts on two different phase spaces. Both of these spaces contain black holes as zero modes. The result for one of these phase spaces is explicitly shown to be isomorphic to $W^{(2)}_3\times W^{(2)}_3$ in first order perturbations.