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

TL;DR

This paper develops new higher-spin gravity theories in three dimensions by extending known symmetries, introducing novel models with spin-3 fields coupled to topological matter, and exploring flat and AdS limits.

Contribution

It generalizes the algebraic framework for higher-spin extensions in three-dimensional gravity, including new models with Maxwell and AdS-Lorentz symmetries.

Findings

Constructed spin-3 extensions of Maxwell and AdS-Lorentz algebras.

Introduced a gravity model coupled to higher-spin topological matter with zero cosmological constant.

Defined two families of higher-spin extensions of three-dimensional Einstein gravity.

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 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.