Higher-spin Chern-Simons theories in odd dimensions

TL;DR

This paper develops consistent higher-spin gauge theories in odd dimensions using Chern-Simons forms, extending Anti-de Sitter groups, and demonstrates their relation to Lovelock gravity and known higher-spin equations.

Contribution

It constructs new higher-spin Chern-Simons theories in odd dimensions with an invariant tensor, linking them to Lovelock gravity and verifying their linearized equations.

Findings

Constructed higher-spin Chern-Simons actions in odd dimensions.

Connected the theories to Lovelock gravity and topological phases.

Verified linearized equations match Fronsdal equations on AdS_4.

Abstract

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. It contains topological as well as non-topological phases. Focusing on D=5 we consider as an example for the latter an AdS_4 x S^1 Kaluza-Klein background. By solving the higher-spin torsion constraints in the case of a spin-3 field, we verify explicitly that the equations of motion reduce in the linearization to the compensator form of the Fronsdal equations on AdS_4.