General Low Energy Dynamics of Supersymmetric Monopoles

TL;DR

This work derives the general low-energy dynamics of monopoles and dyons in $N=2$ and $N=4$ super-Yang–Mills theories using a collective-coordinate expansion on the monopole moduli space. It introduces a novel supersymmetric quantum mechanics that incorporates multiple Higgs vevs and hypermultiplet matter, including a two-form $T$ on the Index bundle and four real sections $K_i$ that encode hypermultiplet effects; the construction reduces to known results via Scherk–Schwarz dimensional reduction. The authors provide explicit forms for the bosonic potential $V=\tfrac12 G^m G^n g_{mn}$, fermionic couplings, and higher-order matter-induced potentials, and they establish holomorphicity and tri-holomorphic Killing constraints ensuring supersymmetry. The framework unifies pure $N=2$ dynamics with hypermultiplet contributions and recovers $N=4$ monopole dynamics as a special case, offering a robust tool for analyzing BPS spectra on the Coulomb branch and their nonperturbative structure.

Abstract

We derive general low energy dynamics of monopoles and dyons in N=2 and N=4 supersymmetric Yang-Mills theories by utilising a collective coordinate expansion. The resulting new kind of supersymmetric quantum mechanics incorporates the effects of multiple Higgs fields, both in the N=2 vector multiplet and hypermultiplets, having non-vanishing expectation values.