Local conformal symmetry and anomalies with antisymmetric tensor field

We consider the trace anomaly, which results from the integration of the massless conformal fermion field with the background of metric and antisymmetric tensor fields. The non-local terms in the anomaly-induced effective action do not depend on the scheme of quantum calculations. On the other hand, total derivative terms in the anomaly and the corresponding local part of the induced action manifest scheme dependence and multiplicative anomaly.