Curves of Marginal Stability and Weak and Strong-Coupling BPS Spectra in $N=2$ Supersymmetric QCD

TL;DR

This paper analyzes the structure of the Coulomb branch in $N=2$ supersymmetric QCD with $SU(2)$ gauge group, identifying the BPS spectra and curves of marginal stability, and confirming the quantum numbers of massless states at singularities.

Contribution

It explicitly determines the global structure of the $SL(2,Z)$ bundle and the BPS spectra inside and outside the curves of marginal stability for various flavors in $N=2$ SQCD.

Findings

Identifies a circle-like curve of marginal stability on the Coulomb branch.

Determines the BPS spectrum inside and outside the curve, matching decay patterns.

Confirms the quantum numbers of massless states at singularities as proposed by Seiberg and Witten.

Abstract

We explicitly determine the global structure of the $SL(2,Z)$ bundle over the Coulomb branch of the moduli space of asymptotically free $N=2$ supersymmetric Yang-Mills theories with gauge group $SU(2)$ when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability on the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.