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

Abstract

We study a semi-local Abelian Higgs sigma model with 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 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 iσ 3 α and a new kind of semi-local Abelian gauge theory arises. The new system admits also a self-dual structure, and when coupled to gravity a second species of cosmic strings enters the scene.