A formulation of domain wall fermions in the Schroedinger functional

TL;DR

This paper develops a formulation for domain wall fermions within the Schroedinger functional framework, confirming its universality and analyzing chiral symmetry breaking effects near boundaries.

Contribution

It introduces a new formulation of domain wall fermions in the Schroedinger functional and verifies its universality and boundary effects through eigenmode analysis.

Findings

Eigenmodes are localized near fifth dimension boundaries.

Bulk chiral symmetry breaking vanishes with increasing fifth dimension.

Boundary-induced chiral symmetry breaking persists near time boundaries.

Abstract

We present a formulation of domain wall fermions in the Schroedinger functional by following the universality argument given by L\"uscher. To check whether the formulation works, we examine the lowest eigenmode of the free domain wall fermion operator. We confirm that the theory belongs to a correct universality class and that the eigenvector is localized near the boundaries of the fifth dimension. We also investigate the chiral symmetry breaking structure of the four dimentional effective operator. We observe that the bulk chiral symmetry breaking disappears for a large fifth dimensional size, while the breaking originated by the boundary effects persists and exponetially decays away from the time boundaries.