Two species of semi-local cosmic strings in Abelian gauged $\mathbb{CP}^2$-sigma models coupled to gravity

TL;DR

This paper explores cosmic string solutions in a gravity-coupled semi-local Abelian Higgs model with belian gauged p^2 scalar fields, revealing two distinct species of strings associated with different charts of p^2.

Contribution

It introduces a new self-dual structure in p^2 sigma models coupled to gravity, leading to the discovery of two different species of cosmic strings.

Findings

Two species of cosmic strings identified in p^2 model

Self-dual and non-self-dual string solutions constructed

Different string types correspond to different charts of p^2

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 $\mathbb{CP}^2$.