The effective action of W_3-gravity

TL;DR

This paper introduces a new method for deriving the effective action in theories with $W_3$-gravity, using anomalous Ward identities and demonstrating it with supergravity examples.

Contribution

It proposes a novel approach to integrate Ward identities and construct covariant effective actions for $W_3$-gravity and supergravity.

Findings

New operator linking physical quantities to Ward identities

Covariant effective action for matter in $W_3$-gravity background

Method demonstrated with two-dimensional supergravity

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 field interacting with a gravitational and $W_3$-gravitational background is proposed.