Domain-wall fermions and chiral symmetries

TL;DR

This paper analyzes the chiral properties of domain-wall fermions, addressing inconsistencies in recent numerical results by deriving a connecting formula and proposing a solution to clarify chiral symmetry breaking in DWQCD.

Contribution

It derives a new formula linking chiral symmetry breaking to the Wilson-Dirac operator and proposes a solution to reconcile conflicting numerical findings.

Findings

Derived a formula connecting chiral symmetry breaking to the Wilson-Dirac operator.

Proposed a solution that resolves inconsistencies in recent numerical results.

Provided a coherent understanding of chiral properties in DWQCD.

Abstract

We investigate chiral properties of the domain-wall fermion (DWF) system. After a brief introduction for the DWF, we summarize the recent numerical results on the chiral properties of the domain-wall QCD (DWQCD), which seem mutually inconsistent. We next derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four-dimensional hermitian Wilson-Dirac operator. Based on this formula, we propose a solution, which resolves the inconsistency among recent numerical data, and give a consistent picture of the chiral properties of the DWQCD.