Domain wall fermions

Abstract

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).

Figures (7)

• Figure 1: The triangle anomaly. The vertex on the left represents the divergence of the singlet axial current in the regularized theory. For domain wall fermions, it is $J_{5q}$.
• Figure 2: Tadpole correction in one-loop lattice perturbation theory.
• Figure 3: Setting sun diagram, the dominant contribution to the quantum wave function of the domain wall quark.
• Figure 4: Mixing of $J_{5q}^a$ with $J_5^a$, or $J_{5q}$ with $J_5$.
• Figure 5: Mixing of $J_{5q}$ with $J_5$ only.