Large-n Limit of N=2 Supersymmetric Q^n Model in Two Dimensions

TL;DR

This paper explores the non-perturbative vacuum structure of a two-dimensional N=2 supersymmetric sigma model on a Hermitian symmetric space, revealing two stable vacua with different symmetry-breaking mechanisms.

Contribution

It introduces a large-n analysis of the N=2 supersymmetric sigma model on Q^{n-2}(C), discovering a new Higgs phase vacuum not previously known in such models.

Findings

Both vacua are asymptotically free.

No massless Nambu-Goldstone bosons appear despite symmetry breaking.

Identification of a novel Higgs phase vacuum in the model.

Abstract

We investigate non-perturbative structures of the two-dimensional N=2 supersymmetric nonlinear sigma model on the quadric surface Q^{n-2}(C) = SO(n)/SO(n-2)xU(1), which is a Hermitian symmetric space, and therefore Kahler, 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 supersymmetric CP^{n-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.