Monopole and Dyon Bound States in N=2 Supersymmetric Yang-Mills Theories

TL;DR

This paper investigates the existence of monopole and dyon bound states in N=2 supersymmetric Yang-Mills theories, linking their existence to the topology of index bundles and confirming predictions of BPS states through an index theorem.

Contribution

It provides a rigorous proof for the existence of specific BPS monopole and dyon bound states using an $L^2$ index theorem, supporting Seiberg and Witten's vacuum structure predictions.

Findings

Existence of monopole bound states confirmed

Topological analysis of index bundles used

Supports Seiberg-Witten predictions

Abstract

We study the existence of monopole bound states saturating the BPS bound in N=2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an $L^2$ index theorem, we prove the existence of certain BPS states predicted by Seiberg and Witten based on their study of the vacuum structure of N=2 Yang-Mills theories.