# Perfect Lattice Actions with and without Chiral Symmetry

## TL;DR

This paper constructs perfect lattice actions for fermions and gauge fields using continuum blocking, analyzing the effects of chiral symmetry preservation or breaking on locality and gauge invariance, with applications to QCD.

## Contribution

It introduces a method to derive perfect lattice actions via continuum blocking, exploring the impact of chiral symmetry on locality and gauge invariance, and proposes an optimized RG transformation for QCD.

## Key findings

- Chirally symmetric actions are nonlocal but preserve chiral symmetry.
- Breaking chiral symmetry yields local actions with explicit symmetry breaking.
- The spectrum matches the continuum, and anomalies are correctly reproduced.

## Abstract

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.