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arXiv · 0705.3714

Higher-spin Chern-Simons theories in odd dimensions

Johan Engquist·Olaf Hohm
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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.

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Johan Engquist, Olaf Hohm. 2007-07-17. Higher-spin Chern-Simons theories in odd dimensions. https://doi.org/10.1016/j.nuclphysb.2007.06.015

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