A common geometrical context for the instanton, the two-dimensional O(4) sigma model and the skyrmion

Abstract

Topological structures in gauge theories, e.g. monopoles and instantons, may be classified by either Chern classes or winding numbers. On the other hand, Wess-Zumino terms in sigma models are winding number densities and there exists a common mathematical structure for the instanton and the Wess-Zumino term in the two-dimensional O(4) sigma model. The same formalism describes the skyrmion topological Lagrangian in the four-dimensional SU(3) sigma model.