New Chern-Simons densities in both odd and even dimensions

TL;DR

This paper introduces new Chern-Simons densities applicable in all dimensions, including even ones, derived through a process involving dimensional reduction and further descent of Chern-Pontryagin densities.

Contribution

It presents a novel construction of Chern-Simons densities in both odd and even dimensions using dimensional reduction and descent methods.

Findings

New Chern-Simons densities defined in all dimensions

Applicable to Yang-Mills and Higgs fields

Extends the framework to even-dimensional spacetimes

Abstract

After reviewing briefly the dimensional reduction of Chern--Pontryagin densities, we define new Chern--Simons densities expressed in terms of Yang-Mills and Higgs fields. These are defined in all dimensions, including in even dimensional spacetimes. They are constructed by subjecting the dimensionally reduced Chern--Pontryagin densites to further descent by two steps.