The BPS Spectra and Superconformal Points in Massive N=2 Supersymmetric QCD

We present a detailed study of the analytic structure, BPS spectra and superconformal points of the $N=2$ susy $SU(2)$ gauge theories with $N_f=1,2,3$ massive quark hypermultiplets. We compute the curves of marginal stability with the help of the explicit solutions for the low energy effective actions in terms of standard elliptic functions. We show that only a few of these curves are relevant. As a generic example, the case of $N_f=2$ with two equal bare masses is studied in depth. We determine the precise existence domains for each BPS state, and show how they are compatible with the RG flows. At the superconformal point, where two singularities coincide, we prove that (for $N_f=2$) the massless spectrum consists of four distinct BPS states and is S-invariant. This is due to the monodromy around the superconformal point being S, providing strong evidence for exact S-duality of the SCFT. For all $N_f$, we compute the slopes $\omega$ of the $\beta$-functions at the fixed point couplings and show that they are related to the anomalous dimensions $\alpha$ of $u= < tr \phi^2 >$ by $\omega= 2 (\alpha -1)$.