Path-integral quantization of $W_\infty$ gravity

TL;DR

This paper investigates the anomalies in $W_ ablafty$ gravity using path-integral quantization, deriving ghost-loop anomalies to all orders and demonstrating anomaly cancellation between matter and ghost sectors.

Contribution

It provides a comprehensive derivation of all-order ghost-loop anomalies in $W_ ablafty$ gravity and shows how anomaly cancellation ensures consistency of the theory.

Findings

Ghost-loop anomalies derived to all orders in $ abla$-order

Anomaly cancellation between matter and ghost sectors

Path-integral measure and Wess-Zumino consistency used for anomaly analysis

Abstract

We consider the anomalies of $W_\infty$ gravity in the context of path-integralquantization. We derive the ghost-loop anomalies to all orders in $\hbar$ directly from the path-integral measure by the Fujikawa method. We also show that in the matter sector the higher-loop anomalies can be obtained by implementation of the Wess-Zumino consistency condition using the one-loop anomaly. Cancellation of the anomalies between these two sectors then leaves the theory anomaly-free.