A perturbative construction of lattice chiral fermions

We perform a renormalization group transformation to construct perturbatively a lattice theory of chiral fermions. The field variables of the continuum theory are averaged over hypercubes to define lattice fields. Integrating out the continuum variables we derive a chirally invariant effective action for the lattice fields. This is consistent with the Nielsen-Ninomiya theorem because the effective action is nonlocal. We also construct the axial current on the lattice and we show that the axial anomaly of the continuum theory is reproduced in the Schwinger model.