Magnetically Charged Calorons with Non-Trivial Holonomy

TL;DR

This paper explores the structure and properties of magnetically charged calorons with non-trivial holonomy in Yang-Mills theories, providing explicit constructions and mechanisms for net magnetic charge formation.

Contribution

It introduces new analytical constructions of magnetically charged calorons with non-trivial holonomy, including a specific $(2,1)$-caloron with intrinsic magnetic charge.

Findings

Constructed explicit gauge configurations of magnetically charged calorons.

Identified mechanisms for net magnetic charge emergence in calorons.

Provided analytical examples with $U(1)$-symmetry.

Abstract

Instantons in pure Yang-Mills theories on partially periodic space $\mathbb{R}^3\times S^1$ are usually called calorons. The background periodicity brings on characteristic features of calorons such as non-trivial holonomy, which plays an essential role for confinement/deconfinement transition in pure Yang-Mills gauge theory. For the case of gauge group $SU(2)$, calorons can be interpreted as composite objects of two constituent "monopoles" with opposite magnetic charges. There are often the cases that the two monopole charges are unbalanced so that the calorons possess net magnetic charge in $\mathbb{R}^3$. In this paper, we consider several mechanism how such net magnetic charges appear for certain types of calorons through the ADHM/Nahm construction with explicit examples. In particular, we construct analytically the gauge configuration of the $(2,1)$-caloron with $U(1)$-symmetry, which has intrinsically magnetic charge.