On the BPS spectrum at the root of the Higgs Branch

We study the BPS spectrum and walls of marginal stability of the N = 2 supersymmetric theory in four dimensions with gauge group SU(n) and n ≤ Nf < 2n fundamental flavours at the root of the Higgs branch. The strong-coupling spectrum of this theory was conjectured in hep-th/9902134 to coincide with that of the two-dimensional supersymmetric CP2n−Nf−1 sigma model. Using the Kontsevich–Soibelman wall-crossing formula, we start with the conjectured strong-coupling spectrum and extrapolate it to all other regions of the moduli space. In the weak-coupling regime, our results precisely agree with the semiclassical analysis of hep-th/9902134: in addition to the usual dyons, quarks, and W bosons, if the complex masses obey a particular inequality, the resulting weak-coupling spectrum includes a tower of bound states consisting of a dyon and one or more quarks. In the special case of Zn-symmetric masses, there are bound states with one quark for odd n and no bound states for even n. a