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

A Generalisation of the Nielsen-Olesen Vortex: Non-cylindrical strings in a modified Abelian-Higgs model