Calorons and constituent monopoles

TL;DR

This paper investigates calorons, which are anti-self-dual Yang-Mills instantons on b3b7S^{1}, analyzing their structure as the circle collapses and revealing their decomposition into monopole constituents, with a general construction for various Lie groups.

Contribution

It provides a detailed decomposition of calorons into monopole constituents and a uniform gluing construction applicable to any compact semi-simple Lie group.

Findings

Explicit decomposition of calorons into monopoles as the circle shrinks.

A gluing construction for calorons from monopole constituents.

Computation of the moduli space dimension for calorons.

Abstract

We study anti-self-dual Yang-Mills instantons on $\mathbb{R}^{3}\times S^{1}$, also known as calorons, and their behaviour under collapse of the circle factor. In this limit, we make explicit the decomposition of calorons in terms of constituent pieces which are essentially charge $1$ monopoles. We give a gluing construction of calorons in terms of the constituents and use it to compute the dimension of the moduli space. The construction works uniformly for structure group an arbitrary compact semi-simple Lie group.