Higgs-Chern-Simons gravity models in 2n+1 dimensions

TL;DR

This paper introduces a new class of Higgs-Chern-Simons gravity models in odd dimensions, generalizing existing models by incorporating scalar and vector fields derived from Higgs-Chern-Pontryagin densities, with some exact solutions found.

Contribution

It develops Higgs-Chern-Simons gravity models in 2n+1 dimensions, extending previous Chern-Simons gravity theories with new fields derived from Higgs-Chern-Pontryagin densities.

Findings

Exact solutions in 3 and 5 dimensions

Generalization of Chern-Simons gravity models

Framework for deriving models from Higgs-Chern-Pontryagin densities

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) gravitaties 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), 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.