Topological defects on manifolds with curvature
[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...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/157893 |
| Acceso en línea: | http://hdl.handle.net/10366/157893 |
| Access Level: | acceso abierto |
| Palabra clave: | Tesis y disertaciones académicas Universidad de Salamanca (España) Tesis Doctoral Academic dissertations Ecuaciones en derivadas parciales Solitones 1202.20 Ecuaciones Diferenciales en derivadas Parciales |
| Sumario: | [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. |
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