Perturbative analysis of the Neuberger-Dirac operator in the Schr\"odinger functional

We investigate the spectrum of the free Neuberger-Dirac operator $\text{Dov}$ on the Schr"odinger functional (SF). We check that the lowest few eigen-values of the Hermitian operator ${\text{Dov}}^{\mathrm{†}}\text{Dov}$ in unit of $L^{-2}$ converge to the continuum limit properly. We also perform a one-loop calculation of the SF coupling, and then check the universality and investigate lattice artifacts of the step scaling function. It turns out that the lattice artifacts for the Neuberger-Dirac operator are comparable in those of the clover action.