The coupling of spin-3 gauge fields to three-dimensional Maxwell and $AdS$-Lorentz gravity theories is presented. After showing how the usual spin-3 extensions of the $AdS$ and the Poincar\'e algebras in three dimensions can be obtained as expansions of $\mathfrak{ sl}\left( 3,\mathbb{ R}\right)$ algebra, the procedure is generalized so as to define new higher-spin symmetries. Remarkably, the spin-3 extension of the Maxwell symmetry allows one to introduce a novel gravity model coupled to higher-spin topological matter with vanishing cosmological constant, which in turn corresponds to a flat limit of the $AdS$-Lorentz case. We extend our results to define two different families of higher-spin extensions of three-dimensional Einstein gravity.
Categories: hep-th math-ph math.MP