Schroedinger functional formalism with Ginsparg-Wilson fermion

TL;DR

This paper develops a new method to implement Schroedinger functional boundary conditions with Ginsparg-Wilson fermions, overcoming eigenvalue and locality issues in the overlap Dirac operator.

Contribution

It introduces an orbifolding projection technique to impose boundary conditions on Ginsparg-Wilson fermions, addressing previous difficulties with eigenvalues and locality.

Findings

Successfully imposed boundary conditions using orbifolding

Maintained locality properties of the overlap Dirac operator

Provided a consistent formalism for finite volume fermions

Abstract

The Schroedinger functional formalism is given as a field theory in a finite volume with a Dirichlet boundary condition in temporal direction. When one tries to construct this formalism with the Ginsparg-Wilson fermion including the overlap Dirac operator and the domain-wall fermion one easily runs into difficulties. The reason is that if the Dirichlet boundary condition is simply imposed on the Wilson Dirac operator $DW$ inside of the overlap Dirac operator an exponentially small eigenvalue appears in $DW$, which affects the locality properties of the operator. In this paper we propose a new procedure to impose the Schroedinger functional Dirichlet boundary condition on the overlap Dirac operator using an orbifolding projection.