A formulation of domain-wall fermions in the Schr\"odinger functional

TL;DR

This paper develops a new formulation of domain-wall fermions within the Schr"odinger functional framework, validating its universality, renormalizability, and analyzing chiral symmetry breaking and lattice artifacts through numerical and analytical methods.

Contribution

It introduces a novel formulation of domain-wall fermions in the Schr"odinger functional and investigates its properties using spectrum analysis, one-loop calculations, and comparison with other discretizations.

Findings

Spectrum analysis confirms universality.

One-loop analysis supports renormalizability.

Chiral symmetry breaking arises from bulk and boundary effects.

Abstract

We present a formulation of domain-wall fermions in the Schr\"odinger functional by following a universality argument. To examine the formulation, we numerically investigate the spectrum of the free operator and perform a one-loop analysis to confirm universality and renormalizability. We also study the breaking of the Ginsparg-Wilson relation to understand the structure of chiral symmetry breaking from two sources: The bulk and boundary. Furthermore, we discuss the lattice artifacts of the step scaling function by comparing with other fermion discretizations.