Schroedinger functional formalism with domain-wall fermion

TL;DR

This paper proposes a new orbifolding projection method to implement Schroedinger functional boundary conditions for domain-wall fermions, facilitating non-perturbative renormalization in lattice QCD.

Contribution

It introduces a novel orbifolding projection technique to impose Schroedinger functional boundary conditions on domain-wall fermions, overcoming previous difficulties.

Findings

Successful formulation of boundary conditions for domain-wall fermions

Enables non-perturbative renormalization with domain-wall fermions

Improves finite volume renormalization schemes in lattice QCD

Abstract

Finite volume renormalization scheme is one of the most fascinating scheme for non-perturbative renormalization on lattice. By using the step scaling function one can follow running of renormalized quantities with reasonable cost. It has been established the Schroedinger functional is very convenient to define a field theory in a finite volume for the renormalization scheme. The Schroedinger functional, which is characterized by a Dirichlet boundary condition in temporal direction, is well defined and works well for the Yang-Mills theory and QCD with the Wilson fermion. However one easily runs into difficulties if one sets the same sort of the Dirichlet boundary condition for the overlap Dirac operator or the domain-wall fermion. In this paper we propose an orbifolding projection procedure to impose the Schroedinger functional Dirichlet boundary condition on the domain-wall fermion.