Domain walls and dimensional reduction

Abstract 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 equipped with a mass term with domain-wall-like defects along one of the space-like dimensions, which is moreover compactified. We show that there is a regime such that the only relevant degrees of freedom are massless fermionic fields in D dimensions. For any fixed gauge field configuration, the extra modes may be decoupled, since they can be made arbitrarily heavy. This decoupling combines the usual Kaluza–Klein one, due to the compactification, with a mass enhancement for the non-zero-modes provided by the domain wall mechanism. We obtain quantitative results on the contribution of the massive modes in the cases D =2 and D =4.