Quantum parameter space in super Yang–Mills. II

In [F. Ferrari, ], the author has discussed the quantum parameter space of the N=1 super Yang–Mills theory with one adjoint Higgs field Φ, tree-level superpotential Wtree=mΦ2/2+gΦ3/3, and gauge group U(N). In particular, full details were worked out for U(2) and U(3). By discussing higher rank gauge groups like U(4), for which the classical parameter space has a large number of disconnected components, we show that the phenomena discussed in [F. Ferrari, ] are generic. It turns out that the quantum space is connected. The classical components are related in the quantum theory either through standard singularities with massless monopoles or by branch cuts without going through any singularity. The branching points associated with the branch cuts correspond to new strong coupling singularities, which are not associated with vanishing cycles in the geometry, and at which glueballs can become massless. The transitions discussed recently by Cachazo, Seiberg, and Witten are special instances of those phenomena.