Gauged merons

Abstract

We construct a new class of regular soliton solutions of the gauged planar Skyrme model on the target space S2 with fractional topological charges in the scalar sector. These field configurations represent Skyrmed vortices; they have finite energy and carry topologically quantized magnetic flux Φ=2πn, where n is an integer. Using a special version of the product ansatz as a guide, we obtain by numerical relaxation various multimeron solutions and investigate the pattern of interaction between the fractionally charged solitons. We show that, unlike the vortices in the Abelian Higgs model, the gauged merons may combine short-range repulsion and long-range attraction. Considering the strong gauge coupling limit, we demonstrate that the topological quantization of the magnetic flux is determined by the Poincaré index of the planar components φ¥=φ1+iφ2 of the Skyrme field.