Gauge-Invariant Noncompact Lattice Simulations

TL;DR

This paper introduces three novel gauge-invariant noncompact lattice simulation techniques for nonabelian gauge theories, demonstrating improved confinement signals and gauge invariance properties in numerical experiments.

Contribution

It presents three new methods for gauge-invariant noncompact lattice simulations, including a gauge transformation approach, a gauge symmetrization, and a new invariant action formulation.

Findings

Wilson loops show confinement signals with the first method.

The second method achieves gauge symmetry through group integrations.

The third method provides an exactly gauge-invariant noncompact action.

Abstract

Three techniques for performing gauge-invariant, noncompact lattice simulations of nonabelian gauge theories are discussed. In the first method, the action is not itself gauge invariant, but a kind of lattice gauge invariance is restored by random compact gauge transformations during the successive sweeps of the simulation. This method has been applied to pure $SU(2)$ gauge theory on a $12^4$ lattice, and Wilson loops have been measured at strong coupling, $\beta=0.5$. These Wilson loops display a confinement signal not seen in simulations performed earlier with the same action but without the random gauge transformations. In the second method, the action is gauge symmetrized by integrations over the group manifold. The third method is based upon a new, noncompact form of the action that is exactly invariant under lattice gauge transformations. The action is a natural discretization of the classical Yang-Mills action.