Infrared behavior of Weyl Gravity

TL;DR

This paper explores Quantum Weyl Gravity, analyzing its classical and quantum features, computing the one-loop partition function, and investigating its renormalization group flow, contributing to understanding its quantum consistency and anomalies.

Contribution

It provides a detailed one-loop quantum analysis of Weyl Gravity using physical degrees of freedom and extends previous results on background geometries.

Findings

Computed the one-loop partition function around Einstein spaces.

Reproduced previous renormalization group results on specific backgrounds.

Discussed conformal anomalies and future research directions.

Abstract

In this paper, we introduce and motivate the studies of Quantum Weyl Gravity (also known as Conformal Gravity). We discuss some appealing features of this theory both on classical and quantum level. The construction of the quantum theory is described in detail to the one-loop level. To facilitate computations we use only physical degrees of freedom, which are singled out through the York decomposition. At the one-loop level we compute the partition function around a general Einstein space. Next, the functional renormalization group of couplings in Quantum Weyl Gravity is investigated. We reproduce completely previous results obtained on maximally symmetric and Ricci-flat backgrounds. Finally, we comment on further directions and on the issue of conformal anomaly.