Higgs–Chern–Simons Gravity Models in d = 2n + 1 Dimensions

Abstract

We consider a family of new Higgs–Chern–Simons (HCS) gravity models in 2n+1 dimensions (n=1,2,3). This provides a generalization of the (usual) gravitational Chern–Simons (CS) gravities resulting from non-Abelian CS densities in all odd dimensions, which feature vector and scalar fields, in addition to the metric. The derivation of the new HCS gravitational (HCSG) actions follows the same method as in the usual-CSG case resulting from the usual CS densities. The HCSG result from the HCS densities, which result through a one-step descent of the Higgs–Chern–Pontryagin (HCP), with the latter being descended from Chern-Pontryagin (CP) densities in some even dimension. A preliminary study of the solutions of these models is considered, with exact solutions being reported for spacetime dimensions d=3,5.