Charges of dyons in N=2 supersymmetric gauge theory

TL;DR

This paper derives electric and magnetic charge expressions for dyons in N=2 supersymmetric gauge theories, discusses their role in vacuum transitions, and proposes a minimal set of light dyons necessary for describing these phenomena.

Contribution

It introduces a minimal set of light dyons with specific charge properties that are essential for understanding vacuum transitions in N=2 gauge theories.

Findings

Total number of light dyons equals the product of the gauge group's rank and dual Coxeter number.

A conjecture that this minimal set includes all possible light dyons.

Relation between dyon charges and monodromies at weak and strong couplings.

Abstract

Expressions for electric and magnetic charges of dyons, which become massless in the strong-coupling limit of the supersymmetric N=2 gauge theory with an arbitrary gauge group are presented. Transitions into different vacua of the N =1 gauge theory, when the N=2 supersymmetry is broken explicitly to the N =1 case, are discussed. The existence of a minimal set of light dyons, which are necessary to describe this transition, is established. The total number of these dyons equals the product of the rank and dual Coxeter number of the gauge group. A conjecture, which states that this minimal set incorporates all possible light dyons, is discussed. A relation of dyon charges with monodromies at weak and strong couplings is outlined and comparison with known charges of dyons for particular gauge groups is made.