Abstract
We study a semi-local Abelian Higgs sigma model with $\mathbb{CP}^2$-valued scalar fields coupled to gravity. We establish the conditions needed for self-duality in this system and obtain cosmic strings, both of self-dual character and out of the self-dual point, in the reference chart of $\mathbb{CP}^2$. In any of the other two charts of a minimum atlas, the transition functions break the global $SU(2)$ symmetry to the Abelian subgroup $e^{i \sigma^3 \alpha}$. In this context, using the transition functions a new self-dual structure can be constructed, which defines a second species of cosmic strings. Because of the presence of a potential energy for the scalar fields, each species takes values in a different bounded region of the target space and is most naturally described using a particular chart of $\mathbb{CP}^2$.
Highlights
We study a semilocal Abelian Higgs sigma model with CP2-valued scalar fields coupled to gravity
Topological defects [1] are long lasting solutions of spontaneously broken field theories whose stability is due to the existence of topologically disconnected sectors in the field configuration space, a property inherited from the nontriviality of certain homotopy group of the vacuum manifold V, depending on the dimension of the space and the symmetry of the defect
The core of the string is a filament of false vacuum which carries a mass per unit length μ of order v2, where v is the scale of symmetry breaking which, for grand unified theories, is of order
Summary
Topological defects [1] are long lasting solutions of spontaneously broken field theories whose stability is due to the existence of topologically disconnected sectors in the field configuration space, a property inherited from the nontriviality of certain homotopy group of the vacuum manifold V, depending on the dimension of the space and the symmetry of the defect. E.g., grand unified theories (GUTs), the vacuum manifold is a homogeneous coset space
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