On the weak coupling spectrum of N=2 supersymmetric SU(n) gauge theory

TL;DR

This paper investigates the spectrum of BPS states in pure N=2 supersymmetric SU(n) gauge theory at weak coupling, revealing a domain structure with wall-crossing phenomena and consistency with strong coupling solutions.

Contribution

It introduces a method to analyze the weak coupling spectrum using known N=4 dyon spectra and monodromy actions, uncovering domain structures and decay walls.

Findings

Weak coupling spectrum divided into domains with different dyon charges

Walls where dyons decay separate these domains

Spectrum consistent with strong coupling singularities

Abstract

The weak coupling spectrum of BPS saturated states of pure $N=2$ supersymmetric SU$(n)$ gauge theory is investigated. The method uses known results on the dyon spectrum of the analogous theory with $N=4$ supersymmetry, along with the action on these states of the semi-classical monodromy transformations. For dyons whose magnetic charge is not a simple root of the Lie algebra, it is found that the weak coupling region is divided into a series of domains, for which the dyons have different electric charge, separated by walls on which the dyons decay. The proposed spectrum is shown to be consistent with the exact solution of the theory at strong coupling in the sense that the states at weak coupling can account for the singularities at strong coupling.