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We construct the Schr\"odinger Functional (SF) setup for the M\"obius domainwall fermions (MDWF). The method is an extension of the method proposed byTakeda for the standard domain wall fermion. In order to fulfill therequirement that the lattice Dirac operator with the SF boundary obeys theL\"uscher's universality argument: the lattice chiral fermion with the SFboundary condition breaks the chiral symmetry at the temporal boundary, weimpose the parity symmetry with respect to the fifth-direction on the MDWFoperator. This additional symmetry restricts the choice of the parameter of theMDWF so that the optimal parameter from the Zolotarev optimal approximationcannot be applied. We introduce a modified parameter set having thefifth-dimensional parity symmetry. We investigate the MDWF with the SF boundaryby observing eigenvalues of the Hermitian operator and the Ginsparg-Wilsonrelation violation at the tree-level. We compare the computational cost withthat of the standard DWF with the SF scheme.

A construction of the Schr\"odinger Functional for M\"obius Domain Wall Fermions