SU(2) Calorons and Magnetic Monopoles

TL;DR

This paper explores SU(2) calorons on R^3×S^1, revealing they are composed of two magnetic monopoles, and provides explicit constructions and analysis of their moduli space.

Contribution

It constructs explicit SU(2) caloron solutions using the Nahm method and analyzes their monopole composition and moduli space structure.

Findings

Calorons are composed of two self-dual monopoles of opposite magnetic charge.

Explicit field configurations for single instantons are constructed.

The moduli space metric of instantons is normalized and studied.

Abstract

We investigate the self-dual Yang-Mills gauge configurations on $R^3\times S^1$ when the gauge symmetry SU(2) is broken to U(1) by the Wilson loop. We construct the explicit field configuration for a single instanton by the Nahm method and show that an instanton is composed of two self-dual monopoles of opposite magnetic charge. We normalize the moduli space metric of an instanton and study various limits of the field configuration and its moduli space metric.