Simple look at supersymmetric N=2 gauge theory with arbitrary gauge group

Abstract

A new discrete symmetry is shown to govern and simplify low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary gauge group. Each element of the related symmetry 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 concurrent permutation of r monopoles, provided the sets of charges and monopoles are chosen properly. The superpotential is symmetric under S_r. This symmetry strongly manifests itself for the degenerate case; when the masses of r electric charges are chosen to be equal, then the masses of r monopoles are necessarily degenerate as well, and vice versa. This condition uniquely defines the vital for the theory VEV of the scalar field, which makes all monopoles massless.