Some aspects of Skyrme–Chern–Simons densities

Abstract

Abstract The gauge transformation properties of the Skyrme–Chern–Simons (SCS) densities is studied. Two types of SCS actions are identified, typeI in which the gauge group is smaller than the largest possible one, and typeII which are gauged with the largest allowed gauge group. TypeI SCS feature only one power of the gauge connection and no curvature, while typeII feature both the gauge connection and the curvature. The abelian typeI SCS turn out to be explicitly gauge invariant while non-abelian typeI and all typeII 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.