Discontinuous BPS Spectra in N=2 Susy QCD

These notes are based on work done in collaboration with Frank Ferrari. We show how to determine the spectra of stable BPS states in $N=2$ supersymmetric $SU(2)$ Yang-Mills theories that are asymptotically free, i.e. without and with $N_f=1,2,3$ quark hypermultiplets. In all cases: $\bullet$ There is a curve of marginal stability diffeomorphic to a circle and going through all (finite) singular points of moduli space. $\bullet$ The BPS spectra are discontinuous across these curves. $\bullet$ The strong-coupling spectra (inside the curves) contain only those BPS states that can become massless and are responsible for the singularities. Except for $N_f=3$, they form a multiplet (with different masses) of the broken global discrete symmetry. $\bullet$ All other semi-classical BPS states must and do decay consistently when crossing the curves. $\bullet$ The weak-coupling, i.e. semi-classical BPS spectra, contain no magnetic charges larger than one for $N_f=0,1,2$ and no magnetic charges larger than two for $N_f=3$.