A scaling study of the step scaling function in SU(3) gauge theory with improved gauge actions

TL;DR

This study examines the scaling behavior of the step scaling function in SU(3) gauge theory using improved gauge actions, confirming consistency with previous results and analyzing effects of boundary terms and cutoff dependence.

Contribution

It provides a detailed comparison of improved gauge actions and their scaling behavior, demonstrating universality and the impact of boundary counter terms in continuum extrapolation.

Findings

Improved gauge actions agree with plaquette action results in the continuum limit.

Cutoff dependence is reduced with perturbative scaling violations correction.

The low energy scale ratio shows universality across actions.

Abstract

We study the scaling behavior of the step scaling function for SU(3) gauge theory, employing the renormalization-group improved Iwasaki gauge action and the perturbatively improved L\"uscher-Weisz gauge action. We confirm that the step scaling functions from the improved gauge actions agree with that previously obtained from the plaquette action within errors in the continuum limit at both weak and strong coupling regions. We also investigate how different choices of boundary counter terms for the improved gauge actions affect the scaling behavior. In the extrapolation to the continuum limit, we observe that the cut off dependence becomes moderate for the Iwasaki action, if a perturbative reduction of scaling violations is applied to the simulation results. We also measure the low energy scale ratio with the Iwasaki action, and confirm its universality.