Strings in Yang-Mills-Higgs theory coupled to gravity

Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly constructed. We consider $N_f$ Higgs fields in the fundamental representation of the $U(1)\times SU(N_c)$ gauge group in order to have a color-flavor $SU(N_c)$ group remaining unbroken. Choosing a suitable ansatz for the metric, Bogomol’nyi-like first-order equations are found and rotationally symmetric solutions are proposed. In the $N_f=N_c$ case, solutions are local strings and are shown to be truly non-Abelian by parametrizing them in terms of orientational collective coordinates. When $N_f>N_c$, the solutions correspond to semilocal strings which, beside the orientational degrees of freedom, acquire additional collective coordinates parametrizing their transverse size. The low-energy effective theories for the correspondent moduli are found, showing that all zero modes are normalizable in presence of gravity, even in the semilocal case.