Domain walls and dimensional reduction

TL;DR

This paper investigates a dimensional reduction mechanism for fermions using domain wall defects in odd-dimensional spacetimes, showing how massless fermions in lower dimensions emerge by decoupling massive modes.

Contribution

It demonstrates a regime where only massless fermions remain relevant after dimensional reduction, combining compactification and domain wall effects to decouple extra modes.

Findings

Massless fermions dominate in the reduced D-dimensional theory.

Massive modes can be made arbitrarily heavy and decoupled.

Quantitative analysis provided for D=2 and D=4 cases.

Abstract

We study some properties of a dimensional reduction mechanism for fermions in an odd number D+1 of spacetime dimensions. A fermionic field is equipped with a mass term with domain wall like defects along one of the spacelike 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.