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

Jin Chen

Department of Physics, University of Minnesota, Minneapolis, MN 55455, USA

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Xiaoyi Cui

Mathematisches Institut, Georg-August Universität Göttingen, Göttingen, D-37073, Germany

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Mikhail Shifman

Department of Physics, University of Minnesota, Minneapolis, MN 55455, USA

William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA

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, and

Arkady Vainshtein

Department of Physics, University of Minnesota, Minneapolis, MN 55455, USA

William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA

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https://doi.org/10.1142/S0217751X16501475Cited by:6 (Source: Crossref)

Abstract

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 $𝒩 = (0, 1)$ 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 $𝒩 = (0, 1)$ models with the $S^{N - 1} = SO (N) / SO (N - 1)$ target space while preserving the isometries. This also includes $CP (1)$ (equivalent to $S^{2}$ ) 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.

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