Chiral property of domain-wall fermion from eigenvalues of 4D Wilson-Dirac Operator

TL;DR

This paper analyzes the chiral properties of domain-wall fermions using eigenvalues of the 4D hermitian Wilson-Dirac operator, deriving a formula that explains numerical results and discussing large-volume behavior.

Contribution

It introduces a formula linking the Ward-Takahashi identity quark mass to eigenvalues of the Wilson-Dirac operator, clarifying the chiral properties of DWF.

Findings

Derived a formula for $m_{5q}$ in terms of eigenvalues.

Explained the $N_5$ dependence of $m_{5q}$ observed numerically.

Discussed chiral properties in the large volume limit.

Abstract

We investigate a chiral property of the domain-wall fermion (DWF) system using the four-dimensional hermitian Wilson-Dirac operator $H_W$. A formula expressing the Ward-Takahashi identity quark mass $m_{5q}$ with eigenvalues of this operator is derived, which well explains the $N_5$ dependence of $m_{5q}$ observed in previous numerical simulations. We further discuss the chiral property of DWF in the large volume in terms of the spectra of $H_W$.