Discrete symmetry in supersymmetric N=2 gauge theory

TL;DR

This paper discovers a new discrete symmetry group in N=2 supersymmetric gauge theory that links electric charges and monopoles, influencing the theory's low-energy properties and mass degeneracies.

Contribution

It introduces a novel discrete symmetry group S_r in N=2 gauge theory, relating electric charges and monopoles, and extends Seiberg-Witten analysis to arbitrary gauge groups.

Findings

The symmetry group S_r permutes electric charges and monopoles.

Degeneracy of monopole masses implies degeneracy of electric charges.

Identifies the scalar field VEV where all monopoles become massless.

Abstract

A new discrete symmetry group, which governs low-energy properties of the supersymmetric N=2 gauge theory is found. Each element of this group S_r, r being the rank of the gauge group, represents a permutation of r electric charges available in the theory accompanied by a simultaneous permutation of r monopoles, provided the sets of charges and monopoles are chosen properly. Properties of the theory are strongly influenced by S_r; if the central charges (and masses) of r monopoles are degenerate, then the central charges (and masses) of r electric charges are also necessarily degenerate, and vice versa. This condition uniquely defines the vital value of the VEV of the scalar field, at which all monopoles are massless. The general theoretical discussion is illustrated by a model, which generalizes the Seiberg-Witten treatment of the supersymmetric N=2 gauge theory for an arbitrary gauge group.