Monopole Dynamics and BPS Dyons N=2 Super-Yang-Mills Theories

TL;DR

This paper analyzes the low energy monopole dynamics in N=2 super-Yang-Mills theories, revealing how the BPS spectrum depends on electric charge signs and matches Seiberg-Witten theory predictions.

Contribution

It provides a detailed derivation of monopole dynamics with potential terms and explores the BPS spectrum in SU(3) theories using Dirac operators on Taub-NUT space.

Findings

BPS spectrum depends on electric charge signs

Hypermultiplets are consistent with Seiberg-Witten theory

Supersymmetric quantum mechanics governs monopole dynamics

Abstract

We determine the low energy dynamics of monopoles in pure N=2 Yang-Mills theories for points in the vacuum moduli space where the two Higgs fields are not aligned. The dynamics is governed by a supersymmetric quantum mechanics with potential terms and four real supercharges. The corresponding superalgebra contains a central charge but nevertheless supersymmetric states preserve all four supercharges. The central charge depends on the sign of the electric charges and consequently so does the BPS spectrum. We focus on the SU(3) case where certain BPS states are realised as zero-modes of a Dirac operator on Taub-NUT space twisted by the tri-holomorphic Killing vector field. We show that the BPS spectrum includes hypermultiplets that are consistent with the strong- and weak-coupling behaviour of the Seiberg-Witten theory.