Magnetic Monopole Dynamics, Supersymmetry, and Duality

TL;DR

This paper reviews the properties, dynamics, and quantum states of supersymmetric magnetic monopoles, emphasizing their classical solutions, moduli space structure, and D-brane realizations in supersymmetric Yang-Mills theories.

Contribution

It provides a comprehensive overview of BPS monopoles, their low-energy dynamics, and the D-brane perspective, including new insights into multimonopole solutions and their quantum states.

Findings

Detailed analysis of monopole moduli space and metrics

Extension to non-Abelian gauge symmetry cases

Description of quantum BPS states and D-brane realizations

Abstract

We review the properties of BPS, or supersymmetric, magnetic monopoles, with an emphasis on their low-energy dynamics and their classical and quantum bound states. After an overview of magnetic monopoles, we discuss the BPS limit and its relation to supersymmetry. We then discuss the properties and construction of multimonopole solutions with a single nontrivial Higgs field. The low-energy dynamics of these monopoles is most easily understood in terms of the moduli space and its metric. We describe in detail several known examples of these. This is then extended to cases where the unbroken gauge symmetry include a non-Abelian factor. We next turn to the generic supersymmetric Yang-Mills (SYM) case, in which several adjoint Higgs fields are present. Working first at the classical level, we describe the effects of these additional scalar fields on the monopole dynamics, and then include the contribution of the fermionic zero modes to the low-energy dynamics. The resulting low-energy effective theory is itself supersymmetric. We discuss the quantization of this theory and its quantum BPS states, which are typically composed of several loosely bound compact dyonic cores. We close with a discussion of the D-brane realization of ${\cal N}=4$ SYM monopoles and dyons and explain the ADHMN construction of monopoles from the D-brane point of view.