# Construction of lattice M\"obius domain wall fermions in the Schr\"odinger functional scheme

## TL;DR

This paper constructs M"obius domain wall fermions within the Schr"odinger functional scheme for SU(3) gauge theory, analyzing their spectral properties and one-loop beta function contributions through perturbation theory.

## Contribution

It introduces a boundary operator to implement MDWFs in the SF scheme and investigates their universality and perturbative properties.

## Key findings

- Spectrum universality at tree-level
- Fermionic contribution reproduces the universal one-loop beta function
- Effective operator properties confirmed in perturbation theory

## Abstract

In this paper we construct the M\"obius domain wall fermions (MDWF) in the Schr\"odinger functional (SF) scheme for the SU(3) gauge theory by adding a boundary operator at the temporal boundary of the SF scheme setup and investigate the property using the perturbation theory. The MDWFs we investigated include the optimal type domain wall, the overlap, the truncated domain wall, and the truncated overlap fermions. We observe the universality of the spectrum of the effective four-dimensional operator at the tree-level. The fermionic contribution to the universal one-loop beta function is reproduced for the MDWFs with a sufficiently large fifth dimensional extent.