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

TL;DR

This paper tackles the weak-coupling BPS spectrum of pure $N=2$ SU($n$) gauge theory by leveraging the known $N=4$ dyon spectrum and semi-classical monodromies. It shows that the weak-coupling region splits into curves of marginal stability (CMS) for dyons with non-simple magnetic charges, and constructs a minimal yet consistent spectrum where dyons with simple-root magnetic charges exist across the weak coupling, while non-simple-root dyons populate CMS-separated domains. The strong-coupling solution, encoded by a hyperelliptic curve, is used to validate the weak-coupling spectrum; the massless dyons at strong coupling correspond to vanishing cycles whose charges appear in the weak-coupling spectrum, and the associated monodromies match semiclassical expectations. Overall, the work provides a coherent framework linking weak- and strong-coupling dynamics for higher-rank gauge groups, with CMS serving as a crucial organizing principle and with open questions remaining about strong-coupling CMS geometry and direct semi-classical quantization.

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.