  Starting from an anomaly-free Abelian Higgs model coupled to gravity in a
6-dimensional space-time we construct an effective four-dimensional theory of
charged fermions interacting with U(1) Abelian gauge field and gravity, both
localised near the core of a Nielsen-Olesen vortex configuration. We show that
an anomaly free theory in 6-dimensions can give rise to an anomalous theory in
D=4, which suggests a possibility of consistent regularisation of abelian
anomalous chiral gauge theories in four dimensions. We also show that the
spectrum of charged bulk fermions has a mass gap.
