Moduli spaces with external fields

We consider the geometric structures on the moduli space of static finite energy solutions to the 2+12+1-dimensional unitary chiral model with the Wess–Zummino–Witten (WZW) term. It is shown that the magnetic field induced by the WZW term vanishes when restricted to the moduli spaces constructed from the Grassmannian embeddings, so that the slowly moving solitons can in some cases be approximated by a geodesic motion on a space of rational maps from CP1CP1 to the Grassmannian.