Dimensional reduction, magnetic flux strings, and domain walls

Abstract

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 $QE{D}_4$, with fermions confined to a plane, deriving the effective action that describes the `planar' system.

22 pages, LaTeX

References in corpus (3)

• Induced Parity Breaking Term at Finite Temperature
• Dirac Fermions and Domain Wall Defects in 2+1 Dimensions
• Dynamical Domain Wall Defects in 2+1 Dimensions

Cited by in corpus (3)

• Zero modes in non local domain walls
• Anomaly cancellation in three-dimensional noncommutative gauge theories
• Interacting fermions and domain wall defects in 2+1 dimensions