On Isometry Anomalies in Minimal N=(0,1) and N=(0,2) Sigma Models

Abstract

The two-dimensional minimal supersymmetric sigma models with homogeneous target spaces $G/H$ and chiral fermions of the same chirality are revisited. We demonstrate that the Moore-Nelson consistency condition revealing a global anomaly in CP(N-1) (with N>2 and $\mathcal{N}=(0,2)$ supersymmetry) due to a nontrivial first Pontryagin class is in one-to-one correspondence with the local anomalies of isometries in these models. These latter anomalies are generated by fermion loop diagrams which we explicitly calculate. In the case of O}(N) sigma models the first Pontryagin class vanishes, so there is no global obstruction for the minimal $\mathcal{N}=(0,1)$ supersymmetrization of these models. We show that at the local level isometries in these models are anomaly free. Thus, there are no obstructions to quantizing the minimal $\mathcal{N}=(0,1)$ models with the $S^{N-1}=SO(N)/SO(N-1)$ target space. This also includes CP(1) (equivalent to $S^2$) which is an exceptional case from the CP(N-1) series. We also discuss a relation between the geometric and gauged formulations of the CP}(N-1) models.

28 pages, 2 figures

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