Asymptotic Symmetry Algebras in Non-Anti-de-Sitter Higher-Spin Gauge Theories

We analyze asymptotic symmetry algebras in (2+1)-dimensional non-AdS higher-spin gravity with a focus on AdS${}_2\times \mathbb{R}$ and ${\mathbb{H}}_2\times \mathbb{R}$. We find a consistent set of boundary conditions for spin-3 gravity in the non-principal embedding and calculate the corresponding asymptotic symmetry algebra in the classical and quantum mechanical case. In addition, we check for unitary representations of the resulting quantum ${\mathcal{W}}_3^{(2)}$ algebra and give an interpretation of the corresponding CFT.