Perfect Lattice Actions with and without Chiral Symmetry

Details Perfect Lattice Actions with and without Chiral Symmetry Perfect Lattice Actions with and without Chiral Symmetry

1995-09-15

arxiv.org/abs/hep-lat/9509052v2

Nucl.Phys.Proc.Suppl. 47 (1996) 575-582

Physics

High Energy Physics

High Energy Physics - Lattice

LaTex, 8 pages, Contribution to Lattice 95; Some minor typing errors are corrected

Scientific paper

10.1016/0920-5632(96)00125-9

We use perturbation theory to construct perfect lattice actions for fermions 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 chirally symmetric but nonlocal. When the renormalization group transformation breaks chiral symmetry, the lattice action becomes local but chiral symmetry is explicitly broken. In particular, starting with a chiral gauge theory in the continuum one either obtains a lattice theory which is gauge invariant but nonlocal, or a local theory with explicitly broken gauge invariance. In both cases the spectrum of the lattice theory is identical with the one of the continuum and the anomaly is correctly reproduced. We also apply our techniques to vector-like theories. In particular we propose a new renormalization group transformation for QCD and we optimize its parameters for locality of the perfect action.

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