An Improved Single-Plaquette Gauge Action

TL;DR

This paper introduces a nonperturbatively improved single-plaquette gauge action for 4-d SU(2) and SU(3) theories, significantly reducing lattice artifacts and improving accuracy without requiring fine lattice spacing.

Contribution

The authors develop and test a new gauge action that suppresses large plaquette fluctuations, leading to drastically reduced cut-off effects in lattice gauge theory simulations.

Findings

Significant reduction of lattice artifacts observed.

Coarse lattice results closely match continuum values.

Estimated 40-fold improvement in statistical accuracy and artifact suppression.

Abstract

We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-off effects. The simplicity of the gauge action makes it amenable for dynamical fermion simulations.