235 research outputs found
Multimonopoles and closed vortices in SU(2) Yang-Mills-Higgs theory
We review classical monopole solutions of the SU(2) Yang-Mills-Higgs theory.
The first part is a pedagogical introduction into to the basic features of the
celebrated 't Hooft - Polyakov monopole. In the second part we describe new
classes of static axially symmetric solutions which generalise 't Hooft -
Polyakov monopole. These configurations are either deformations of the
topologically trivial sector or the sectors with different topological charges.
In both situations we construct the solutions representing the chains of
monopoles and antimonopoles in static equilibrium. The solutions of another
type are closed vortices which are centred around the symmetry axis and form
different bound systems. Configurations of the third type are monopoles bounded
with vortices. We suggest classification of these solutions which is related
with 2d Poincare index.Comment: 34 pages, 8 figures. Invited contribution prepared for Review Volume
"Etudes on Theoretical Physics" dedicated to 65th anniversary of the
Department of Theoretical Physics, Belarus State University, Minsk. Based on
a work in collaboration with Jutta Kunz and Burkhard Kleihaus. Any comments
and suggestions, especially with respect to references, are welcom
Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential
We construct new solutions of the Faddeev-Skyrme model with a symmetry
breaking potential admitting vacuum. It includes, as a limiting case, the
usual symmetry breaking mass term, another limit corresponds to the
potential , which gives a mass to the corresponding component of
the scalar field. However we find that the spacial distribution of the energy
density of these solutions has more complicated structure, than in the case of
the usual Hopfions, typically it represents two separate linked tubes with
different thicknesses and positions. In order to classify these configurations
we define a counterpart of the usual position curve, which represents a
collection of loops corresponding to the
preimages of the points , respectively. Then
the Hopf invariant can be defined as . In this model, in the sectors of degrees
we found solutions of new type, for which one or both of these tubes
represent trefoil knots. Further, some of these solutions possess different
types of curves and .Comment: 22 pages, 129 figure
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