SU(2) Lattice Gauge Theory with Logarithmic Action: Scaling and Universality

TL;DR

This paper studies an SU(2) lattice gauge theory with a logarithmic action, demonstrating confinement and universality with the standard Wilson action, and analyzing its scaling behavior and topological features.

Contribution

It introduces a logarithmic action for SU(2) lattice gauge theory and shows it shares the same universality class as the Wilson action, with distinct scaling properties.

Findings

The model exhibits confinement, contrary to previous claims.

It belongs to the same universality class as the Wilson action.

The $eta$-function is monotonic, similar to the positive plaquette model.

Abstract

We investigate a version of SU(2) lattice gauge theory with a logarithmic action. The model is found to exhibit confinement, contrary to previous claims in the literature. Comparing ratios of physical quantities, like $\sqrt{\sigma}/T_c$, we find that the model belongs to the same universality class as the standard SU(2) lattice gauge theory with Wilson action. Like the positive plaquette model, the model with logarithmic action has a monotonic $\beta$-function, without the famous dip exhibited by the Wilson action. Short distance dislocations affecting the definition of topology are slightly more suppressed than for the positive plaquette model.