Existence and stability of pure Faddeev-Hopf instantons
The Faddeev-Hopf model will be considered in the strong coupling limit where only the Faddeev-Skyrme term is significant. This field theory generalizes naturally to the case of any Riemannian domain and Kaehler codomain. It has key similarities to Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. We will develop the variational calculus in the general geometric setting, leading to strong results on existence and stability of finite energy solutions of the model. For example, we will show that all immersive solutions are stable, and that there are no non-vacuum immersive solutions on the 4-sphere.
Joint work with Martin Svensson (Odense).