PERFECT LATTICE ACTIONS WITH AND WITHOUT CHIRAL-SYMMETRY

We use perturbation theory to construct perfect lattice actions for fe rmions and gauge fields by blocking directly from the continuum. When one uses a renormalization group transformation that preserves chiral symmetry the resulting lattice action for massless fermions is chirall y symmetric but nonlocal. When the renormalisation group transformatio n breaks chiral symmetry the lattice action becomes local but chiral s ymmetry is explicitly broken. In particular, starting with a chiral ga uge theory in the continuum one either obtains a lattice theory which is gauge invariant but nonlocal, or a local theory with explicitly bro ken gauge invariance. In both cases the spectrum of the lattice theory is identical with the one of the continuum and the anomaly is correct ly reproduced. We also apply our techniques to vector-like theories. I n particular we propose a new renormalization group transformation for QCD and we optimize its parameters for locality of the perfect action .