Fixed Point Actions for Wilson Fermions

TL;DR

This paper derives fixed point actions for Wilson fermions through renormalization group transformations, revealing a line of fixed points with local actions that improve lattice QCD scaling and a nonlocal, chirally invariant endpoint action that evades fermion doubling.

Contribution

It analytically computes fixed point actions for Wilson fermions, including a nonlocal, chirally invariant action that avoids fermion doubling, advancing lattice chiral fermion formulations.

Findings

Identified a line of fixed points for Wilson fermions.

Computed fixed point actions analytically.

Discussed use of nonlocal fixed point action for chiral fermions.

Abstract

Iterating renormalization group transformations for lattice fermions the Wilson action is driven to fixed points of the renormalization group. A line of fixed points is found and the fixed point actions are computed analytically. They are local and may be used to improve scaling in lattice QCD. The action at the line's endpoint is chirally invariant and still has no fermion doubling. The Nielsen-Ninomiya theorem is evaded because in this case the fixed point action is nonlocal. The use of this action for a construction of lattice chiral fermions is discussed.