Abstract
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.
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Campoleoni, A., Fredenhagen, S., Pfenninger, S. et al. Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields. J. High Energ. Phys. 2010, 7 (2010). https://doi.org/10.1007/JHEP11(2010)007
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DOI: https://doi.org/10.1007/JHEP11(2010)007