The effective action of W 3-gravity

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. Zh. éksp. Teor. Fiz. 111, 1537–1553 (May 1997)