Perturbative analysis of the Neuberger-Dirac operator in the Schr\"odinger functional

TL;DR

This paper analyzes the spectral properties of the Neuberger-Dirac operator within the Schrödinger functional framework, performs a one-loop calculation of the coupling, and compares lattice artifacts to other actions.

Contribution

It provides a perturbative analysis of the Neuberger-Dirac operator's spectrum and lattice artifacts, demonstrating their similarity to the clover action.

Findings

Eigenvalues converge to the continuum limit

Lattice artifacts are comparable to the clover action

Universality of the step scaling function is confirmed

Abstract

We investigate the spectrum of the free Neuberger-Dirac operator $\Dov$ on the Schr\"odinger functional (SF). We check that the lowest few eigen-values of the Hermitian operator $\Dov^{\dag}\Dov$ in unit of $L^{-2}$ converge to the continuum limit properly. We also perform a one-loop calculation of the SF coupling, and then check the universality and investigate lattice artifacts of the step scaling function. It turns out that the lattice artifacts for the Neuberger-Dirac operator are comparable in those of the clover action.