Noncompact Gauge-Invariant Lattice Simulations

TL;DR

This paper introduces a new gauge-invariant, noncompact Monte Carlo simulation method for lattice gauge theories, successfully reproducing known results and demonstrating confinement in non-Abelian theories.

Contribution

The paper presents a novel noncompact, gauge-invariant Monte Carlo approach applicable to $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on lattices, with results matching exact and perturbative predictions.

Findings

Accurate $U(1)$ Wilson loop ratios for $eta \,\geq\, 1$

Observation of quark confinement at specific couplings for $SU(2)$ and $SU(3)$

Agreement with perturbation theory at weak coupling after renormalization

Abstract

We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$ lattices. The Creutz ratios of the Wilson loops agree with the exact results for $U(1)$ for $\beta \ge 1$ apart from a renormalization of the charge. The $SU(2)$ and $SU(3)$ Creutz ratios robustly display quark confinement at $\beta = 0.5$ and $\beta = 1.5$, respectively. At much weaker coupling, the $SU(2)$ and $SU(3)$ Creutz ratios agree with perturbation theory after a renormalization of the coupling constant.