Formulation of domain-wall fermions in the Schrödinger functional

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 the boundary. Furthermore, we discuss the lattice artifacts of the step scaling function by comparing with other fermion discretizations.