Perfect Gauge Actions on Anisotropic Lattices

TL;DR

This paper explores constructing classically perfect SU(3) gauge actions on anisotropic lattices to reduce lattice artifacts, using two methods and parametrizing with anisotropic smeared links, achieving small renormalization effects.

Contribution

It introduces two methods for constructing anisotropic classically perfect actions for SU(3) gauge theory and demonstrates their effectiveness with minimal renormalization.

Findings

Constructed anisotropic perfect actions with anisotropy 2.

Measured small renormalization of anisotropy.

Used parametrization with anisotropic APE-like smeared links.

Abstract

On anisotropic lattices, where generally the lattice is rather coarse in spatial directions, a parametrized classically perfect action could help reducing lattice artifacts considerably. We investigate the possibility of constructing such actions for SU(3) gauge theory. We present two different methods to do so, either repeating the procedure used to create our newly parametrized isotropic FP action, or performing one single step starting with the isotropic result. The anisotropic action is parametrized using an ansatz including anisotropically APE-like smeared (``fat'') links. The parametrized classically perfect action with anisotropy $\xi=a_s/a_t=2$ is constructed and the renormalized anisotropy is measured using the torelon dispersion relation. It turns out that the renormalization is small.