Test of the Schr\"odinger functional with chiral fermions in the Gross-Neveu model

The recently proposed construction of chiral fermions on lattices with boundaries is tested in an interacting theory up to first order of perturbation theory. We confirm that, in the bulk of the lattice, the chiral Ward identities take their continuum value up to cutoff effects without any tuning. Universal quantities are defined that have an expansion in the renormalised couplings with coefficients that are functions of the physical size and the periodicity in the spatial direction. These coefficient functions have to be identical for different discretisations. We find agreement with the standard Wilson fermions. The computation is done in the asymptotically free Gross-Neveu model with continuous chiral symmetry.