Confining dyon gas with finite-volume effects under control

TL;DR

This paper analytically and numerically investigates a non-interacting dyon ensemble to understand confinement in non-Abelian gauge theories, demonstrating linear quark-antiquark potential growth and controlling finite-volume effects with Ewald's method.

Contribution

It provides an analytical derivation of the linear potential from a non-interacting dyon model and applies Ewald's summation to manage finite-volume effects in numerical simulations.

Findings

Quark-antiquark free energy grows linearly with distance.

String tension scales with dyon density.

Finite-volume effects are effectively controlled using Ewald's method.

Abstract

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T < T_c, we consider a non-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles.