Perfect Gauge Actions on Anisotropic Lattices

TL;DR

This paper develops a method to construct classically perfect anisotropic SU(3) gauge actions on lattices, accurately determining physical quantities and demonstrating the effectiveness of the approach for different anisotropies.

Contribution

It introduces a new explicit construction method for anisotropic perfect gauge actions based on isotropic fixed point actions, with detailed parametrization and validation.

Findings

Renormalised anisotropy is small and well-controlled.

The method accurately reproduces physical quantities like the static potential and glueball spectrum.

The approach is effective for anisotropies of 2 and 4.

Abstract

We present a method for constructing classically perfect anisotropic actions for SU(3) gauge theory based on a present isotropic Fixed Point Action. The action is parametrised using smeared (``fat'') links. The construction is done explicitly for anisotropy $\xi=a_s/a_t=2,4$ and the renormalised anisotropies are determined using the torelon dispersion relation. Quantities such as the static quark-antiquark potential, the critical temperature of the deconfining phase transition and the low-lying glueball spectrum are measured as well. It turns out that the procedure presented works, the renormalised anisotropy is small and the parametrisation describes the full action well. Issues such as the application of the method for scalar fields as well as for the quadratic approximation to gauge theory, measurements of autocorrelation times of simple operators and of the computational overhead are also covered. A (more compact) paper about this classically perfect anisotropic gauge action is in preparation.