Progress on Perfect Lattice Actions for QCD

TL;DR

This paper discusses progress in constructing an approximately perfect lattice action for QCD, improving locality and spectral properties of quarks and gluons, and exploring non-perturbative and topological aspects.

Contribution

It introduces methods to create a near-perfect lattice QCD action with improved locality, spectral accuracy, and topological charge definition, advancing lattice simulation fidelity.

Findings

Short-ranged fermions approximate continuum spectra well

Renormalized heavy quark masses align with continuum physics

Multigrid formulation enhances non-perturbative simulations

Abstract

We describe a number of aspects in our attempt to construct an approximately perfect lattice action for QCD. Free quarks are made optimally local on the whole renormalized trajectory and their couplings are then truncated by imposing 3-periodicity. The spectra of these short ranged fermions are excellent approximations to continuum spectra. The same is true for free gluons. We evaluate the corresponding perfect quark-gluon vertex function, identifying in particular the ``perfect clover term''. First simulations for heavy quarks show that the mass is strongly renormalized, but again the renormalized theory agrees very well with continuum physics. Furthermore we describe the multigrid formulation for the non-perturbative perfect action and we present the concept of an exactly (quantum) perfect topological charge on the lattice.