QED from six-dimensional vortex and gauge anomalies

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.