The large N limit of the Nahm transform

TL;DR

This paper investigates the large N limit of the Nahm transform, revealing a simplification where monopoles approximate magnetic bags and Nahm equations relate to area-preserving vector fields on the sphere.

Contribution

It demonstrates that the Nahm transform simplifies significantly in the large N limit, connecting monopoles to magnetic bags and Lie algebra of area-preserving vector fields.

Findings

Large N monopoles approach magnetic bags.

Nahm equations relate to area-preserving vector fields.

Transform simplifies in the large N limit.

Abstract

We consider the large N limit of the Nahm transform, which relates charge N monopoles to solutions to the Nahm equation involving NxN matrices. In the large N limit the former approaches a magnetic bag, and the latter approaches a solution of the Nahm equation based on the Lie algebra of area-preserving vector fields on the 2-sphere. We show that the Nahm transform simplifies drastically in this limit.