Aspects of Domain-Wall Fermion on the Lattice

TL;DR

This paper introduces transparent boundary layers in the fifth dimension for domain-wall fermions, ensuring exact chiral symmetry and continuum-like behavior of observables regardless of gauge fields.

Contribution

It proposes a novel boundary layer setup that preserves chiral symmetry exactly in lattice domain-wall fermions, aligning lattice observables with continuum symmetries.

Findings

Exact chiral projection in lattice fermions

Symmetry preservation independent of gauge fields

Improved continuum correspondence of lattice observables

Abstract

Two transparent layers are introduced at the boundaries of the fifth dimension for the optimal domain-wall fermions. For the quark fields defined in terms of these two transparent layers, they obey the usual chiral projection rule in the continuum, independent of the gauge fields. Consequently, any observable constructed with the quark fields manifests the symmetries exactly as those of its counterpart in the continuum.