Magnetic Domains

TL;DR

This paper explores the mathematical and physical properties of magnetic bags and their Nahm transform, connecting them to string theory, higher gauge theories, and large n limits of monopoles and M-branes.

Contribution

It extends the Nahm transform to higher gauge theories and arbitrary domains, providing new insights into magnetic bags and their relation to string theory and M-branes.

Findings

Nahm transform for magnetic bags is interpreted via string theory.

Bags in four dimensions relate to large n limit of self-dual strings.

Basu-Harvey equation is the large n limit of an M2-brane equation.

Abstract

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.