Classically Perfect Gauge Actions on Anisotropic Lattices

TL;DR

This paper develops a method to construct classically perfect anisotropic gauge actions for SU(3) using smeared links, enabling precise measurements of physical quantities like glueball masses on anisotropic lattices.

Contribution

It introduces a new explicit construction of classically perfect anisotropic actions for SU(3) gauge theory based on isotropic fixed point actions, with detailed parametrisation and validation.

Findings

Renormalised anisotropies are close to target values.

Accurate measurements of glueball masses and static potential.

Small renormalisation of the anisotropy.

Abstract

We present a method for constructing classically perfect anisotropic actions for SU(3) gauge theory based on an isotropic Fixed Point Action. The action is parametrised using smeared (``fat'') links. The construction is done explicitly for anisotropy $\xi=a_s/a_t=2$ and 4. The corresponding renormalised anisotropies are determined using the torelon dispersion relation. The renormalisation of the anisotropy is small and the parametrisation describes the true action well. Quantities such as the static quark-antiquark potential, the critical temperature of the deconfining phase transition and the low-lying glueball spectrum are measured on lattices with anisotropy $\xi=2$. The mass of the scalar $0^{++}$ glueball is determined to be 1580(60) MeV, while the tensor $2^{++}$ glueball is at 2430(60) MeV.