On the BPS Spectrum at the Root of the Higgs Branch

Details On the BPS Spectrum at the Root of the Higgs Branch On the BPS Spectrum at the Root of the Higgs Branch

2012-02-25

arxiv.org/abs/1202.5595v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 4 figures

Scientific paper

We study the BPS spectrum and walls of marginal stability of the $\mathcal{N}=2$ supersymmetric theory in four dimensions with gauge group SU(n) and $n\le N_{f}<2n$ 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 $\mathbb{CP}^{2n-N_{f}-1}$ 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 $\mathbb{Z}_{n}$-symmetric masses, there are bound states with one quark for odd $n$ and no bound states for even $n$.

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