Canonical charges and asymptotic symmetry algebra of conformal gravity

TL;DR

This paper investigates the canonical structure and asymptotic symmetries of four-dimensional conformal gravity, establishing finite, conserved charges for diffeomorphisms and clarifying the algebraic structure of boundary-preserving transformations.

Contribution

It constructs gauge generators and charges in conformal gravity with generalized boundary conditions, showing the absence of Weyl charge and identifying the asymptotic symmetry algebra.

Findings

Charges are finite and conserved for diffeomorphisms.

No charge associated with Weyl transformations.

Asymptotic symmetry algebra matches boundary-preserving diffeomorphisms.

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.