Magnetic monopole loops generated from calorons with nontrivial holonomy

Abstract

We study whether or not magnetic monopoles are generated from calorons defined in the space $\mathbb{R}^3\times S^1$ with the period $\beta$. We give numerical evidence that one-caloron solution with nontrivial holonomy generates two loops of magnetic monopole and each loop passing through one of the two poles of the caloron winds along the time direction for small $\beta$, while two loops approach each other to fuse into an unwinding loop for large $\beta$, suggesting the existence of a critical value of $\beta$ separating two different phases. This work is a first step to explain quark confinement/deconfinement at finite temperature from the viewpoint of dual superconductor picture in our framework.