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Higher-Spin Chern-Simons Theories in odd Dimensions

By Johan Engquist and Olaf Hohm


We construct consistent bosonic higher-spin gauge theories in odd dimensions D> 3 based on Chern-Simons forms. The gauge groups are infinitedimensional 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 AdS4 × 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 Frønsdal equation

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