Canonical charges and asymptotic symmetry algebra of conformal gravity

Abstract

We study canonical conformal gravity in four dimensions and construct the gauge generators and the associated charges. Using slightly generalized boundary conditions compared to those in \cite{Grumiller:2013mxa} we find that the charges associated with space-time diffeomorphisms are finite and conserved in time. They are also shown to agree with the Noether charges found in \cite{Grumiller:2013mxa}. However, there exists no charge associated with Weyl transformations. Consequently the asymptotic symmetry algebra is isomorphic to the Lie algebra of the boundary condition preserving diffeomorphisms. For illustrative purposes we apply the results to the Mannheim--Kazanas--Riegert solution of conformal gravity.