Connections between non-abelian gravitating vortex equations and electroweak non-abelian cosmic strings

Determine whether the non-abelian gravitating vortex equations, obtained via dimensional reduction of the Kähler–Yang–Mills–Higgs equations using vortex vector bundles, have connections to non-abelian cosmic strings arising from the electroweak theory, by establishing whether a precise mathematical or physical correspondence exists.

Background

The paper constructs examples of solutions to the non-abelian gravitating vortex equations on the sphere, derived from a dimensional reduction of the Kähler–Yang–Mills–Higgs equations with vortex vector bundles. These equations generalize the gravitating vortex framework that has been linked to cosmic strings in earlier abelian contexts.

Motivated by the role of cosmic strings in field theory and prior links between abelian gravitating vortices and self-dual Einstein–Maxwell–Higgs equations, the authors remark on a potential connection in the non-abelian setting to electroweak-theory cosmic strings. However, they explicitly state that whether such a connection exists is currently unknown.