Scaling limits of periodic monopoles

TL;DR

This paper investigates the behavior of singly periodic SU(2) monopoles as their size-to-period ratio varies, revealing complex transitional structures between small monopole chains and large, nearly two-dimensional configurations.

Contribution

It provides new insights into the structure and transition phenomena of periodic monopoles, especially for the charge 2 case, across different size-to-period ratios.

Findings

Identifies the transition from small monopole chains to large, 2D-like configurations.

Discovers unintuitive dependence on the periodic direction during the transition.

Focuses on the detailed structure of charge 2 monopoles.

Abstract

The purpose of this note is to explore the structure of singly periodic monopoles for different values of the size to period ratio. The transition between a chain of small monopoles and the approximately two dimensional chain of large monopoles takes us through a region with an unintuitive dependence on the periodic direction. The focus is mainly on the smooth SU(2) monopole of charge 2.