Summary: 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 “á 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 \(\text{QED}_4\), with fermions confined to a plane, deriving the effective action that describes the “planar” system.