From Perturbation Theory to Confinement: How the String Tension is built up

TL;DR

This paper investigates how the string tension in SU(2) Yang-Mills theory emerges from perturbative regimes to confinement, showing that finite volume effects are minimal and the string tension approaches the infinite volume limit.

Contribution

It provides a detailed analysis of the volume dependence of electric flux energies, connecting perturbative results to the confinement regime with twisted boundary conditions.

Findings

String tension is close to the infinite volume value at small volumes (~1.2 fm^3)

Electric flux energies smoothly approach rotational invariance

Finite volume effects are minimal for confinement properties

Abstract

We study the spatial volume dependence of electric flux energies for SU(2) Yang-Mills fields on the torus with twisted boundary conditions. The results approach smoothly the rotational invariant Confinement regime. The would-be string tension is very close to the infinite volume result already for volumes of $(1.2 \ {\rm fm.})^3$. We speculate on the consequences of our result for the Confinement mechanism.