On isometry anomalies in minimal = (0, 1) and = (0, 2) sigma models

The two-dimensional minimal supersymmetric sigma models with homogeneous target spaces G/H and chiral fermions of the same chirality are revisited. In particular, we look into the isometry anomalies in O(N) and CP(N - 1) models. These 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 = (0, 1) supersymmetrization of these models. We show that at the local level isometries in these models can be made anomaly free by specifying the counterterms explicitly. Thus, there are no obstructions to quantizing the minimal = (0, 1) models with the SN-1 = SO(N)/SO(N - 1) target space while preserving the isometries. This also includes CP(1) (equivalent to S2) which is an exceptional case from the CP(N - 1) series. For other CP(N - 1) models, the isometry anomalies cannot be rescued even locally, this leads us to a discussion on the relation between the geometric and gauged formulations of the CP(N - 1) models to compare the original of different anomalies. A dual formalism of O(N) model is also given, in order to show the consistency of our isometry anomaly analysis in different formalisms. The concrete counterterms to be added, however, will be formalism dependent.