Gauged Skyrme analogue of Chern-Pontryagin

An analogue of the Chern-Pontryagin density for $SO(D)$ gauged $O(D+1)$ Skyrme systems, referred to as Skyrme–Chern-Pontryagin (SCP) densities is known for dimensions $D=2,3,4$. Since these are defined only through a prescription, it is necessary to extend the realisation to higher $D$, which is carried out here for $D=5$. The construction of SCP densities in $D=2,3,4,5$ is presented here in a unified pattern with the aim of pointing out to the possible extrapolation to all dimensions.