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 Poincaré 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.

version 3, 28 pages, accepted version in Nuclear Physics B

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Cited by in corpus (36)

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