Domain walls and dimensional reduction

We study some properties of a dimensional reduction mechanism for fermions in an odd number D + 1 of space-time dimensions. A fermionic field is equip ped with a mass term with domain-wall-like defects along one of the space-l ike dimensions, which is moreover compactified. We show that there is a reg ime such that the only relevant degrees of freedom are massless fermionic f ields in D dimensions. For any fixed gauge field configuration, the extra m odes may be decoupled, since they can be made arbitrarily heavy. This decou pling combines the usual Kaluza-Klein one, due to the compactification, wit h a mass enhancement for the non-zero-modes provided by the domain wall mec hanism. We obtain quantitative results on the contribution of the massive m odes in the cases D = 2 and D = 4. (C) 1999 Elsevier Science B.V. All right s reserved.