Topological Solitons Seminar: Hopf solitons and integrable theories in 3 + 1 dimensions
20 January 2010 14:15 in CM221
It is believed that hidden symmetries may play an important role in the understanding of many non-perturbative aspects of field theories. On the other hand, it is known that the existence of solitons in 1+1 dimensions depends crucially on the hidden symmetries described by flat connections. Solitons in higher dimensions are not well understood yet from that point of view. We discuss the development of an approach to construct theories with an infinite number of conservation laws and based on flat connections in loop spaces. As an application we discuss the example of the so-called extended Skyrme-Faddeev model providing its zero curvature representation which leads to the existence of an integrable sub-sector with an infinite number of conserved currents. Exact vortex and hopfion solutions are constructed in that sector. Numerical hopfion solutions are also constructed.
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