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.