Dimensional reduction, magnetic flux strings, and domain walls

We study some consequences of dimensionally reducing systems with massless fermions and Abelian gauge fields from 3 + 1 to 2 + 1 dimensions. We first consider fermions in the presence of an external Abelian gauge field. In th e reduced theory, obtained by compactifying one of the coordinates "a la Ka luza-Klein", magnetic Bur strings are mapped into domain wall defects. Ferm ionic zero modes, localized around the flux strings of the 3 + 1 dimensiona l theory, become also zero modes in the reduced theory, via the Callan and Harvey mechanism, and are concentrated around the domain wall defects. We a lso study a dynamical model: massless QED(4), with fermions confined to a p lane, deriving the effective action that describes the "planar" system. (C) 2000 Elsevier Science B-V. All rights reserved.