AdS Chern-Simons gravity induces conformal gravity

The leitmotif of this paper is the question of whether four- and higher even-dimensional conformal gravities do have a Chern-Simons pedigree. We show that Weyl gravity can be obtained as the dimensional reduction of a five-dimensional Chern-Simons action for a suitable (gauge-fixed, tractorlike) five-dimensional anti-de Sitter connection. The gauge-fixing and dimensional reduction program readily admits a generalization to higher dimensions for the case of certain conformal gravities obtained by contractions of the Weyl tensor.