Chiral properties of domain-wall fermions from eigenvalues of 4 dimensional Wilson-Dirac operator

TL;DR

This paper explores the chiral symmetry properties of domain-wall fermions by analyzing the eigenvalues of the four-dimensional Wilson-Dirac operator, deriving formulas that relate eigenvalues to chiral symmetry breaking, and discussing behavior as the fifth dimension grows.

Contribution

It introduces a formula linking chiral symmetry breaking in domain-wall fermions to the eigenvalues of the Wilson-Dirac operator, simplifying analysis in terms of eigenvalues.

Findings

Derived a formula connecting chiral symmetry breaking to eigenvalues.

Analyzed the behavior of chiral symmetry as the fifth dimension lengthens.

Discussed the chiral property in the infinite volume and fifth-dimensional limits.

Abstract

We investigate chiral properties of the domain-wall fermion (DWF) system by using the four-dimensional hermitian Wilson-Dirac operator. We first derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator, and simplify the formula in terms of only the eigenvalues of the operator, using an ansatz for the form of the eigenvectors. For a given distribution of the eigenvalues, we then discuss the behavior of the chiral symmetry breaking term as a function of the fifth dimensional length. We finally argue the chiral property of the DWF formulation in the limit of the infinite fifth dimensional length, in connection with spectra of the hermitian Wilson-Dirac operator in the infinite volume limit as well as in the finite volume.