Domain wall fermions

We introduce the formulation of domain wall fermions in the context of lattice QCD. We prove the recovery of exact chiral symmetry in the limit of an infinite fifth direction, and derive the effective four-dimensional operator satisfying the Ginsparg-Wilson relation obtained in this limit. We discuss the residual breaking of chiral symmetry for finite extent of the fifth direction, and how it is affected by spectral features of the Wilson kernel. We also discuss various improvements of domain wall fermions including notably Möbius fermions. These notes are a chapter contributed to the on-line book ``Lattice QCD at 50 years’’ (LQCD@50).