Abstract
A new method for integrating anomalous Ward identities and finding the effective action is proposed. Two-dimensional supergravity and W 3-gravity are used as examples to demonstrate its potential. An operator is introduced that associates each physical quantity with a Ward identity, i.e., a quantity that is transformed without anomalous terms and can be nullified in a consistent manner. A covariant form of the action for matter fields interacting with a gravitational and W 3-gravitational background is proposed.
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