The SU(2) Gauge Field Theory of Magnetic Skyrmion

The theoretical research of the origin of magnetic skyrmion is very interesting. In 2-dim magnetic materials, the existence of magnetic skyrmion is closely related to the SU(2) gauge transformation of its every magnetization. Studying the gauge parallel condition, SU(2) gauge potential is expressed as flat connection by SU(2) gauge transformation. We obtain the inner topological structure of second Chern number. What's more, we prove that the curvature of U(1) Wu-Yang potential is just the integral kernel of magnetic skyrmion.