Supersymmetric nonlinear sigma models as anomalous gauge theories

TL;DR

This paper investigates supersymmetric nonlinear sigma models on specific target manifolds, revealing the necessity of Wess-Zumino terms for anomaly cancellation, analyzing their behavior at large N, and exploring symmetry breaking and vacuum stability.

Contribution

It introduces a method to determine Wess-Zumino terms in supersymmetric sigma models with anomalous gauge symmetries and analyzes their large-N behavior and vacuum structure.

Findings

Wess-Zumino term is essential for anomaly cancellation in these models.

The models exhibit a critical coupling constant similar to bosonic models.

In the weak coupling regime, U(1) symmetry breaks but supersymmetry remains intact.

Abstract

We revisit supersymmetric nonlinear sigma models on the target manifold $CP^{N-1}$ and $SO(N)/SO(N-2)\times U(1)$ in four dimensions. These models are formulated as gauged linear models, but it is indicated that the Wess-Zumino term should be added to the linear model since the hidden local symmetry is anomalous. Applying a procedure used for quantization of anomalous gauge theories to the nonlinear models, we determine the form of the Wess-Zumino term, by which a global symmetry in the linear model becomes smaller in the action than the conventional one. Moreover, we analyze the resulting linear model in the $1/N$ leading order. Consequently, we find that the model has a critical coupling constant similar to bosonic models. In the weak coupling regime, the $U(1)$ local symmetry is broken but supersymmetry is never broken. In contrast to the bosonic case, it is impossible to find stable vacua in the strong coupling regime as far as in the $1/N$ leading order. These results are straightforwardly generalized to the case of the hermitian symmetric space.