Three generations on a local vortex in extra dimensions

We develop an approach to the origin of three generations of the standard model fermions from one generation in a higher-dimensional theory, where four-dimensional fermions appear as zero modes trapped in the core of a topological defect, and the hierarchy of masses and mixings is produced by wave function overlaps in extra dimensions. We present a model with unbroken U(1) symmetry where three zero modes appear on an Abrikosov–Nielsen–Olesen vortex due to nontrivial scalar-fermion interactions.