Conclusions
- There are Static, Stable Topological Defect solutions even in theories where the homotopy groups of the vacuum and/or the target space are trivial. A class of them includes the Embedded Defects.
- The simplest paradigm of an Embedded Defect is the Semilocal Vortex. It has well defined stability parameter sector.
- The Semilocal Vortex exists also as a Stable Solution in the Standard Electroweak Model of Particle Physics called Electroweak Vortex. The Electroweak Vortex is Unstable for the physically realized values of parameters of the Standard Electroweak Model.
- Non-trivial core structures can develop within Embedded Defects in theories where the enlarged symmetry group gets explicitly broken. Such structures can develop in the core of the embedded Nielsen-Olesen vortex leading to superconductivity and in core of the embedded ‘t Hooft - Polyakov monopole.