Domain wall fermions

TL;DR

This paper introduces domain wall fermions in lattice QCD, demonstrating how chiral symmetry is recovered in the infinite fifth dimension limit and discussing improvements like M"obius fermions.

Contribution

It formalizes domain wall fermions, proves chiral symmetry recovery in the infinite limit, and explores improvements such as M"obius fermions.

Findings

Chiral symmetry is exactly recovered as the fifth dimension becomes infinite.

Residual chiral symmetry breaking depends on spectral features of the Wilson kernel.

Improvements like M"obius fermions enhance the formulation.

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 M\"obius fermions. These notes are a chapter contributed to the on-line book ``Lattice QCD at 50 years'' (LQCD@50).