Higher-spin Chern-Simons theories in odd dimensions

Understand

We construct consistent bosonic higher-spin gauge theories in odd dimensions D>3 based on Chern-Simons forms.

• The gauge groups are infinite-dimensional higher-spin extensions of the Anti-de Sitter groups SO(D-1,2).
• We propose an invariant tensor on these algebras, which is required for the definition of the Chern-Simons action.
• The latter contains the purely gravitational Chern-Simons theories constructed by Chamseddine, and so the entire theory describes a consistent coupling of higher-spin fields to a particular form of Lovelock gravity.