Some aspects of Skyrme--Chern-Simons densities

TL;DR

This paper analyzes the gauge transformation properties of Skyrme--Chern-Simons densities, classifies two types based on gauge groups, and discusses their gauge invariance and potential applications in soliton construction.

Contribution

It introduces a classification of Skyrme--Chern-Simons densities into two types and examines their gauge invariance properties and implications for soliton models.

Findings

Type I SCS are gauge invariant in Abelian case

Type II SCS involve both gauge connection and curvature

SCS are defined in both even and odd dimensions

Abstract

The gauge transformation properties of the Skyrme--Chern-Simons (SCS) densities is studied. Two types of SCS actions are identified, Type_{I} in which the gauge group is smaller than the largest possible one, and Type_{II} which are gauged with the largest allowed gauge group. Type_{I} SCS feature only one power of the gauge connection and no curvature, while Type_{II} feature both the gauge connection and the curvature. The Abelian Type_{I} SCS turn out to be explicitly gauge invariant while non-Abelian Type_{I} and all Type_{II} SCS are gauge invariant only up to a total divergence term, and hence lead to gauge covariant equations of motion. SCS actions are the gauged Skyrmion analogues of the usual Chern-Simons (CS) actions, except that unlike the CS which are defined only in odd dimensions, the SCS are defined also in even dimensions. Some areas of application in the construction of solitons are pointed out.