On the Existence of States Saturating the Bogomol'nyi Bound in N=4 Supersymmetry

TL;DR

This paper demonstrates the existence of certain bound states in N=4 supersymmetric gauge theories that saturate the Bogomol'nyi bound, which is crucial for understanding S-duality in these theories.

Contribution

It provides an argument for the existence of at least one bound state saturating the Bogomol'nyi bound for each coprime electric and magnetic charge in N=4 supersymmetric gauge theories.

Findings

Existence of bound states saturating the Bogomol'nyi bound for coprime charges

Implication for the necessary conditions of S-duality in N=4 theories

Commentary on the uniqueness of such states

Abstract

We give an argument showing that in N=4 supersymmetric gauge theories there exists at least one bound state saturating the Bogomol'nyi bound with electric charge $p$ and magnetic charge $q$, for each $p$ and $q$ relatively prime, and we comment on the uniqueness of such state. This result is a necessary condition for the existence of an exact S-duality in N=4 supersymmetric theories.