Construction of lattice Möbius domain wall fermions in the Schrödinger functional scheme

Abstract

In this paper we construct the Möbius domain wall fermions (MDWF) in the Schrödinger 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.

Comments: 40 pages, 26 figures