Fixed Point Actions for Lattice Fermions

TL;DR

This paper investigates fixed point actions for Wilson and staggered lattice fermions via renormalization group transformations, identifying local and nonlocal fixed points with implications for lattice QCD and fermionic theories.

Contribution

It introduces fixed point actions for Wilson and staggered fermions, revealing their properties and potential for constructing perfect lattice actions in fermionic theories.

Findings

Identification of a line of fixed points for both fermion types.

Existence of very local fixed point actions suitable for perfect lattice actions.

Discovery of a nonlocal fixed point for Wilson fermions related to free chiral fermions.

Abstract

The fixed point actions for Wilson and staggered lattice fermions are determined by iterating renormalization group transformations. In both cases a line of fixed points is found. Some points have very local fixed point actions. They can be used to construct perfect lattice actions for asymptotically free fermionic theories like QCD or the Gross-Neveu model. The local fixed point actions for Wilson fermions break chiral symmetry, while in the staggered case the remnant $U(1)_e \otimes U(1)_o$ symmetry is preserved. In addition, for Wilson fermions a nonlocal fixed point is found that corresponds to free chiral fermions. The vicinity of this fixed point is studied in the Gross-Neveu model using perturbation theory.