Maths HEP Lunchtime Seminars: Existence and stability of pure Hopfions
18 November 2005 13:00 in CM221
"The Faddeev-Hopf (FH) model is a nonlinear sigma model thought to possess knotted string-like solitons in dimension 3. It can be naturally formulated on any Riemannian manifold for a field taking values in any Kaehler manifold. In this talk I will describe the pure FH model, a variant which may be thought of as a strong coupling limit of the original theory, and which has strong similarities with pure Yang-Mills theory. I will give a geometric account of the variational calculus for the model which allows one to construct, and analyze the stability of, many explicit solutions. In particular, I will prove a conjecture of Ward, that the Hopf fibration is a stable solution of the (original) FH model on small 3-spheres."