Chern-Simons Gravities (CSG) and Gravitational Chern-Simons (GCS) densities in all dimensions

TL;DR

This paper introduces Higgs--Chern-Simons densities to generalize Chern-Simons gravities and gravitational Chern-Simons densities to all dimensions, overcoming the odd-dimensional restriction of traditional constructions.

Contribution

It proposes a novel Higgs--Chern-Simons framework that extends the definition of Chern-Simons gravities to all dimensions, including even ones.

Findings

Higgs--Chern-Simons densities are defined in all dimensions.

Extended Chern-Simons gravities are constructed for all dimensions.

Gravitational Chern-Simons densities are extended to all odd dimensions of form 4p-1.

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.