标题： 关于最小的 N=(0,1) 和 N=(0,2) σ 模型中的等距异常 显示英文标题

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

摘要： 具有齐次目标空间$G/H$和相同手征的手征费米子的二维最小超对称sigma模型被重新审视。 我们证明了由于非平凡的第一Pontryagin类而在CP(N-1)（N>2和${\mathcal N}=(0,2)$超对称）中揭示的Moore-Nelson一致性条件所显示的整体反常与这些模型中等距局部反常是一一对应的。 这些后者反常由费米子环图生成，我们明确地计算了它们。 对于O\}(N) sigma模型，第一Pontryagin类消失，因此这些模型的最小${\mathcal N}=(0,1)$超对称化没有全局障碍。 我们表明，在这些模型的局部水平上等距性是没有反常的。 因此，没有障碍来量子化具有$S^{N-1}= SO(N)/SO(N-1)$目标空间的最小${\mathcal N}=(0,1)$模型。 这还包括CP(1)（相当于$S^{2}$），它是CP(N-1)系列的一个特例。 我们还讨论了CP\}(N-1)模型的几何形式和规范形式之间的关系。 显示英文摘要

摘要： 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.