Low Energy Dynamics of N=2 Supersymmetric Monopoles

TL;DR

This paper explores the low-energy behavior of N=2 supersymmetric monopoles, modeling their dynamics with an N=4 supersymmetric quantum mechanics on the monopole moduli space, and links moduli space cohomology to quantum bound states.

Contribution

It generalizes Manton's geodesic approximation to supersymmetric monopoles and connects moduli space cohomology with quantum bound states in N=2 theories.

Findings

Low-energy monopole dynamics described by N=4 supersymmetric quantum mechanics.

Moduli space cohomology classes relate to quantum bound states.

Extension of geodesic approximation to supersymmetric context.

Abstract

It is argued that the low-energy dynamics of $k$ monopoles in N=2 supersymmetric Yang-Mills theory are determined by an N=4 supersymmetric quantum mechanics based on the moduli space of $k$ static monople solutions. This generalises Manton's ``geodesic approximation" for studying the low-energy dynamics of (bosonic) BPS monopoles. We discuss some aspects of the quantisation and in particular argue that dolbeault cohomology classes of the moduli space are related to bound states of the full quantum field theory.