Large-N Limit of N = 2 Supersymmetric QN Model in Two Dimensions

We investigate non-perturbative structures of the two-dimensional N = 2 supersymmet-ric nonlinear sigma model on the quadric surface QN−2(C) = SO(N)/SO(N − 2) × U(1), which is a Hermitian symmetric space, and therefore Kähler, by using the auxiliary field and large-N methods. This model contains two kinds of non-perturbatively stable vacua; one of them is the same vacuum as that of the supersymmetric CPN−1 model, and the other is a new kind of vacuum, which has not yet been known to exist in two-dimensional nonlinear sigma models, the Higgs phase. We show that both of these vacua are asymp-totically free. Although symmetries are broken in these vacua, there appear no massless Nambu-Goldstone bosons, in agreement with Coleman’s theorem, due to the existence of two different mechanisms in these vacua, the Schwinger and the Higgs mechanisms. Non-perturbative analyses in quantum field theories and string theories have been recognized to be necessary to solve important problems which cannot be solved in the frameworks of perturbative theories. In some cases, degenerate vacua that are found to be stable in perturbative analyses turn out to be false vacua as a result o