  We find a emergent azimuthal-angle dependency of the Nielsen-Olesen vortices
in the general relativistic situation just after the symmetry breaking at
GUT-scale. Using a high-frequency perturbation method, we obtain in the first
and second order perturbation equations $\varphi$-dependent terms left over
after the phase transition of the Higgs field. Vortices with high multiplicity
decay into a lattice with entangled Abrikosov vortices. The stability of this
lattice of correlated flux $n=1$ vortices with preferred azimuthal-angle is
guaranteed by the contribution from the bulk spacetime by means of the warp
factor: the cosmic string becomes super-massive for some time during the
evolution and initiates the excitations of the vortices to high multiplicity.
The correlation will not fade away during the expansion by the warp factor. We
used this azimuthal-angle correlation for the explanation of the recently
observed alignment of polarization axes of quasars in large quasar groups. The
detailed behavior of this alignment can be explained with our model. The two
different orientations perpendicular to each other in quasars groups of less
richness could be a second order effect in our model. There is a striking
similarity between this phase transition of the gauged Higgs field and the
temporarily breaking of the axially symmetry of self-gravitating cosmic string,
by the appearance of non-diagonal energy-momentum tensor components. The
eccentricity of the ellipsoid can be seen as order parameter. Recovery to SO(2)
symmetry induces emission of gravitational and electro-magnetic radiation. More
data of high-redshift quasars will be needed in order to test the second order
effect predicted in our model.
