Gauged Skyrme analogue of Chern-Pontryagin

TL;DR

This paper extends the construction of Skyrme--Chern-Pontryagin densities, previously known for dimensions 2 to 4, to dimension 5, aiming for a unified pattern applicable to all dimensions.

Contribution

It provides a unified construction of Skyrme--Chern-Pontryagin densities for dimensions 2 through 5, facilitating potential generalization to all dimensions.

Findings

Constructed SCP densities explicitly for D=5

Unified pattern for SCP densities across D=2,3,4,5

Facilitates extrapolation to higher dimensions

Abstract

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.