General treatment of anomalies in ( 1 , 0 ) and ( 1 , 1 ) two - dimensional super - gravity

In this paper we discuss the interplay among (super-)coordinate, Weyl and Lorentz anomaly both in chiral and non-chiral super-gravity represented by (1, 0) and (1, 1) two-dimensional models. It is shown that for this purpose two regu-larization dependent parameters are needed in the effective action. We discuss in full generality the regularization ambiguities of the induced effective action and recover the corresponding general form of the anomalous Ward Identities. Finally, we explain the difference between chiral and non-chiral super-gravity models in terms of the free parameters and establish relation between these two models by projecting (1, 1) into (1, 0) super-symmetry.