On Monopoles and Domain Walls

TL;DR

This paper explores the mathematical relationship between supersymmetric domain walls and magnetic monopoles, revealing that their moduli spaces are intricately connected through geometric and physical insights.

Contribution

It establishes an isomorphism between the moduli space of domain walls and a submanifold of monopole moduli space using D-brane constructions and Nahm equations.

Findings

Moduli space of domain walls is a complex submanifold of monopole moduli space.

The submanifold is characterized by a circle action fixed point set.

Domain walls correspond to confined monopoles on vortex strings.

Abstract

The purpose of this paper is to describe a relationship between maximally supersymmetric domain walls and magnetic monopoles. We show that the moduli space of domain walls in non-abelian gauge theories with N flavors is isomorphic to a complex, middle dimensional, submanifold of the moduli space of U(N) magnetic monopoles. This submanifold is defined by the fixed point set of a circle action rotating the monopoles in the plane. To derive this result we present a D-brane construction of domain walls, yielding a description of their dynamics in terms of truncated Nahm equations. The physical explanation for the relationship lies in the fact that domain walls, in the guise of kinks on a vortex string, correspond to magnetic monopoles confined by the Meissner effect.