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

Abstract

We investigate non-perturbative structures of the two-dimensional supersymmetric 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 asymptotically 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.