The Geometry of Calorons

TL;DR

This paper explores the extension of the Nahm transform to calorons, which are periodic instantons, providing a new framework for constructing and analyzing these anti-self-dual connections.

Contribution

It introduces a method to extend the Nahm transform to calorons, linking caloron construction to Nahm data on the circle, bridging instantons and monopoles.

Findings

Calorons can be constructed from Nahm data on the circle.

The inverse Nahm transform for calorons is described.

A new correspondence between calorons and Nahm data is established.

Abstract

Calorons (periodic instantons) are anti-self-dual (ASD) connections on S^1 \times R^3 and form an intermediate case between instantons and monopoles. The ADHM and Nahm constructions of instantons and monopoles can be regarded as generalizations of a correspondence between ASD connections on the 4-torus, often referred to as the Nahm transform. This thesis describes how the Nahm transform can be extended to the case of calorons. It is shown how calorons can be constructed from Nahm data similar to that for monopoles, but defined over the circle. The inverse transformation, from the caloron to the Nahm data, is also described.