Schroedinger functional formalism with domain-wall fermion

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 this purpose. 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. Furthermore it matches well with lattice regularization. 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 on lattice. In this paper we propose an orbifolding projection procedure to impose the Schroedinger functional Dirichlet boundary condition on the domain-wall fermion