David Auckly Kansas State University

Topology of a non linear sigma model

The Skyrme model was developed as a nonlinear theory of pions. Since the analytical behavior of the Skyrme model is not well understood, and since there is not much experimental data to test the Skyrme model, various modifications of the Skyrme model are studied. One such modification was proposed by L. Faddeev. This model is described by a functional for maps from a 3-manifold into a 2-sphere. Numerical studies indicate that this model should produce interesting knotted solitons, but very little is known about this functional. In this talk, we will describe work in progress (joint with L. Kapitanski) aimed at proving that there is a mimimizer of the Faddeev functional in each homotopy class of maps.