On the topological charge of SO(2)gauged Skyrmions in 2 +1and 3 +1dimensions

Abstract

The question of the dependence of the topological charge qof a gauged Skyrmion, on the gauge field, is studied quantitatively. Two examples, both gauged with SO(2)are studied and contrasted:i)The O(3) model in 2 +1dimensions, andii)The O(4)model in 3 +1dimensions. In casei), where the (usual) Chern–Simons (CS) term is present, the value of qchanges sign, going through zero. This evolution is tracked by a parameter characterising the solutions in the given theory. In caseii), in which dimensions no CS density is available, the evolution of qis not observed.