Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

We discuss the emergence of $ \mathcal{W} \mbox{-algebras}$ as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) × SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical $ {\mathcal{W}_3}\mbox{-algebra} $ with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant.