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Título
Topological defects on manifolds with curvature
Autor(es)
Director(es)
Materia
Tesis y disertaciones académicas
Universidad de Salamanca (España)
Tesis Doctoral
Academic dissertations
Ecuaciones en derivadas parciales
Solitones
Clasificación UNESCO
1202.20 Ecuaciones Diferenciales en derivadas Parciales
Fecha de publicación
2023
Resumen
[EN] In this thesis different aspects of kinks in non-linear Sigma models are studied.
Sigma models where families of kinks can be analytically identified will be successfully
constructed on different Riemannian manifolds. The stability of these kinks
will also be analysed. Moreover, kinks of field theories in Euclidean spaces will be
geometrically constricted in a continuous manner by extending its target manifold
and choosing interesting families of geometries on it.
On the other hand, Sigma models with analytical solutions will be sought for nonsimply
connected target manifolds. The different homotopy classes of curves that
arise will give rise to the existence of brochosons under certain conditions. This
is, these homotopy classes will allow the existence of non-topological kinks that
cannot decay into vacuum. This will be accomplished by introducing singularities
in the potential in simply connected spaces and by directly considering a non-simply
connected manifold like the torus.
Furthermore, the methods of deformation of Bazeia et al. will be generalised to
the context of Sigma models, also allowing seed-dependent deformations in the process.
Lastly, new methods for identifying kinks in new Sigma models are developed.
On one hand, procedures for cutting and gluing kinks will allow us to design kink
orbits for other Sigma models. In addition to this, Sigma models will be combined
to intertwine their dynamics while retaining the original solutions.
URI
DOI
10.14201/gredos.157893
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