Renormalization of lattice gauge theories with massless Ginsparg Wilson fermions

Abstract

Using functional techniques, we prove, to all orders of perturbation theory, that lattice vector gauge theories with Ginsparg Wilson fermions are renormalizable. For two or more massless fermions, they satisfy a flavour mixing axial vector Ward identity. It involves a lattice specific part that is quadratic in the vertex functional and classically irrelevant. We show that it stays irrelevant under renormalization. This means that in the continuum limit the (standard) chiral symmetry becomes restored. In particular, the flavour mixing current does not require renormalization.