An alternative to domain wall fermions

TL;DR

This paper introduces a new lattice Dirac operator that approximates overlap fermions, offering a potentially more practical alternative to domain wall fermions for numerical QCD simulations.

Contribution

It defines a sparse hermitian lattice Dirac matrix that approximates overlap fermions and provides bounds on its condition number, suggesting a viable alternative to domain wall fermions.

Findings

The new operator approximates the hermitian overlap Dirac operator.

Rigorous bounds on the condition number are established.

Overlap fermions are recommended as a practical alternative to domain wall fermions.

Abstract

We define a sparse hermitian lattice Dirac matrix, $H$, coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of $H$ and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusion is that overlap fermions should be taken seriously as a practical alternative to domain wall fermions in the context of numerical QCD.