Weyl Gravity Revisited

TL;DR

This paper revisits Weyl gravity, exploring its potential for renormalizability and unitarity by analyzing its properties with independent connection and metric variables, and examining effects of external sources.

Contribution

It investigates Weyl gravity's properties with independent variables, highlighting potential for renormalizability and unitarity, and analyzes external source effects.

Findings

No quartic propagators for dynamical variables.

Potential for combining renormalizability and unitarity.

Studied effects of external sources on Weyl gravity.

Abstract

The on shell equivalence of first order and second order formalisms for the Einstein-Hilbert action does not hold for those actions quadratic in curvature. It would seem that by considering the connection and the metric as independent dynamical variables, there are no quartic propagators for any dynamical variable. This suggests that it is possible to get both renormalizability and unitarity along these lines. We have studied a particular instance of those theories, namely Weyl gravity. Although the ground state of this system is difficult to analyze, we have been able to study the physical effects of some external sources.