Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories

TL;DR

This paper compares perturbation theory and Monte Carlo simulations to accurately determine tadpole improvement factors in pure gauge theories, demonstrating perturbation theory's effectiveness and reducing computational effort.

Contribution

It shows two-loop perturbation theory accurately predicts mean links, eliminating the need for numerical tuning of tadpole factors in lattice gauge simulations.

Findings

Two-loop perturbation theory predicts mean links well into typical coupling regions.

A small three-loop coefficient is inferred from simulations.

Finite size effects and Gribov copies are found to be negligible.

Abstract

We calculate the mean link in Landau gauge for Wilson and improved SU(3) anisotropic gauge actions, using two loop perturbation theory and Monte Carlo simulation employing an accelerated Langevin algorithm. Twisted boundary conditions are employed, with a twist in all four lattice directions considerably improving the (Fourier accelerated) convergence to an improved lattice Landau gauge. Two loop perturbation theory is seen to predict the mean link extremely well even into the region of commonly simulated gauge couplings and so can be used remove the need for numerical tuning of self-consistent tadpole improvement factors. A three loop perturbative coefficient is inferred from the simulations and is found to be small. We show that finite size effects are small and argue likewise for (lattice) Gribov copies and double Dirac sheets.