  We modify the standard Abelian-Higgs model by introducing spatially-dependent
couplings for the scalar and vector fields. We investigate static,
non-cylindrically symmetric solutions of the resulting field equations and
propose a pinch solution which interpolates between degenerate vacua along the
string, labelled by $\pm |n|$. This configuration corresponds to a vortex which
shrinks to Planck scale before re-emerging as an anti-vortex, resulting in the
formation of a bead pair with one bead at either side of the intersection. The
solution is then topologically stable. A key assumption is that quantities such
as phase and winding number, along with those which depend on them like the
magnetic flux, become undefined at the Planck scale so that regions of opposite
winding may be joined via a Planck-sized segment of neutral string.
Similarities between this solution and the extra-dimensional windings of
strings in type IIB string theory are discussed and a correspondence between
field theory and string theory parameters is suggested. The spatial-dependence
of the field couplings is found to have a natural interpretation in the dual
string picture and results from the variation of the winding radius, giving
rise to a varying (effective) string coupling. An interesting result is an
estimate of the Higgs mass (at critical coupling) in terms of the parameters
which define the Klebanov-Strassler geometry and which, in principle, may be
constrained by cosmological observations.
