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

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