Anomalies of minimal N=(0,1) and N=(0,2) sigma models on homogeneous spaces

We study chiral anomalies in N= (0, 1) and (0, 2) two-dimensional minimalsigma models defined on the generic homogeneous spaces G/H. Such minimaltheories contain only (left) chiral fermions and in certain cases are inconsistentbecause of incurable? anomalies. We explicitly calculate the anomalous fermioniceffective action and show how to remedy it by adding a series of localcounterterms. In this procedure, we derive a local anomaly matching condition,which is demonstrated to be equivalent to the well-known global topologicalconstraint on_p1 (G H), the first Pontryagin class. More importantly,we show that these local counterterms further modify and constrain curable chiral models, some of which, for example, flow to the nontrivial infraredsuperconformal fixed point. Finally, we also observe an interesting relationbetween N = (0, 1) and (0, 2) two-dimensional minimal sigma models andsupersymmetric gauge theories.