Chern-Simons Gravities (CSG) and Gravitational Chern-Simons (GCS) Densities in All Dimensions

摘要

Chern-Simons gravities and gravitational Chern-Simons densities are constructed using the non-Abelian Yang-Mills Chern-Simons densities. As such, they are defined only in odd dimensions. We propose instead an analogous construction employing what we term Higgs-Chern-Simons (HCS) densities, which are defined in all dimensions. This enables the definition of extended versions of Chern-Simons gravities in all dimensions. Employing the same prescription, the definition of gravitational Chern-Simons densities is extended to all even dimensions, but only to 4p - 1 odd dimensions. All our considerations are restricted to vacuum fields.