Generalized Chern–Simons higher-spin gravity theories in three dimensions

Abstract 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 Poincare algebras in three dimensions can be obtained as expansions of sl ( 3 , R ) 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.