Non perturbative determination of the running coupling constant in quenched SU(2)

TL;DR

This paper uses a finite size renormalization group method to accurately determine the running coupling constant in quenched SU(2) gauge theory across a wide energy range, with minimal lattice artifacts.

Contribution

It introduces a non-perturbative approach based on Polyakov loop correlations with twisted boundary conditions to compute the running coupling in quenched SU(2).

Findings

Achieved a few percent error over a thirtyfold energy range.

Demonstrated smooth extrapolation to the continuum limit.

Quantified lattice artifact corrections proportional to the square of the lattice spacing.

Abstract

Through a finite size renormalization group technique we calculate the running coupling constant for quenched SU(2) with a few percent error over a range of energy varying by a factor thirty. The definition is based on ratio of correlations of Polyakov loops with twisted boundary conditions. The extrapolation to the continuum limit is governed by corrections due to lattice artifacts which are proportional to the square of the lattice spacing and appears rather smooth.