Ward Identities and Anomalies in Pure W_4 Gravity

TL;DR

This paper explores the algebraic structure of W_4 gravity, deriving Ward identities and anomalies by enforcing algebra closure and solving consistency conditions, thus advancing understanding of its symmetries and potential anomalies.

Contribution

It provides a systematic algebraic approach to derive Ward identities and anomalies in pure W_4 gravity, including explicit solutions to consistency conditions.

Findings

Ward identities derived from algebra closure

General forms of anomalies identified

Specific anomaly cases analyzed

Abstract

W_4 gravity is treated algebraically, represented by a set of transformations on classical fields. The Ward identities of the theory are determined by requiring the algebra to close. The general forms for the anomalies are found by looking for solutions to the Wess-Zumino consistency conditions, and some specific cases are considered.