  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 the reduced
theory, obtained by compactifying one of the coordinates `a la Kaluza-Klein,
magnetic flux strings are mapped into domain wall defects. Fermionic zero
modes, localized around the flux strings of the 3+1 dimensional theory, become
also zero modes in the reduced theory, via the Callan and Harvey mechanism, and
are concentrated around the domain wall defects. We also study a dynamical
model: massless $QED_4$, with fermions confined to a plane, deriving the
effective action that describes the `planar' system.

High Energy Physics - Theory