In 5+1 dimensions, we construct a vortex-like solution on a two-dimensional sphere. We study fermionic zero modes in the background of this solution and relate them to the replication of fermion families in the Standard Model. In particular, using a compactified space removes the need for the difficult localisation of gauge fields, while the present procedure (rather than naive compactification on a disk) also removes spurious fermionic modes.

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Abstract. We discuss the notion of mass, mostly for fermions, and its relation to the breaking of CP invariance, the natural symmetry of gauge interactions. In a first model, we show how compactification on a Vortex in 2 extra dimensions leads to a replication of generations in 3+1, with challenging mass patterns, and testable consequences in flavour-changing neutral currents (familynumber conserving), both at low energies and at future colliders. In different model, we show how CP violation can result from compactification from 4+1 to 3+1 dimensions.