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

Abstract

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.