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

TL;DR

This paper reveals a new discrete symmetry in N=2 supersymmetric gauge theories with any gauge group, simplifying low-energy analysis and linking electric charges and monopoles through permutation symmetry.

Contribution

It introduces a permutation symmetry group S_r that governs electric charges and monopoles, providing a new understanding of the scalar field's VEV in N=2 gauge theories.

Findings

Discovered a discrete symmetry group S_r in N=2 gauge theories.

Showed the symmetry relates electric charges and monopoles.

Identified conditions for degenerate masses and massless monopoles.

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.