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 [Formula: see text] and chiral fermions of the same chirality are revisited. In particular, we look into the isometry anomalies in [Formula: see text] and [Formula: see text] models. These anomalies are generated by fermion loop diagrams which we explicitly calculate. In the case of [Formula: see text] sigma models the first Pontryagin class vanishes, so there is no global obstruction for the minimal [Formula: see text] 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 [Formula: see text] models with the [Formula: see text] target space while preserving the isometries. This also includes [Formula: see text] (equivalent to [Formula: see text]) which is an exceptional case from the [Formula: see text] series. For other [Formula: see text] 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 [Formula: see text] models to compare the original of different anomalies. A dual formalism of [Formula: see text] 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.