We formulate four-dimensional conformal gravity with (Anti-)de Sitter boundary conditions that are weaker than Starobinsky boundary conditions, allowing for an asymptotically subleading Rindler term concurrent with a recent model for gravity at large distances. We prove the consistency of the variational principle and derive the holographic response functions. One of them is the conformal gravity version of the Brown-York stress tensor, the other is a 'partially massless response'. The on-shell action and response functions are finite and do not require holographic renormalization. Finally, we discuss phenomenologically interesting examples, including the most general spherically symmetric solutions and rotating black hole solutions with partially massless hair.

We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the new theories with a finite number of higher spin fields, much as in the massless case. The action has the Chern-Simons form for a higher spin extension of the conformal algebra. In general, the new theories contain Fradkin-Tseytlin fields with higher derivatives in the gauge transformations, which is reminiscent of partially-massless fields. A relation of the old and new theories to the parity anomaly is pointed out.

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 [1] 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 [1]. 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.

We evaluate the 1-loop partition function of conformal gravity in four dimensions around an AdS4 background, using the heat kernel techniques. We give expressions for the relevant thermodynamical quantities and compare our results with the ones from the literature. Contents

Canonical charges and asymptotic symmetries in four dimensional conformal gravity I. Lovrekovic PoS(CORFU2014)155 Canonical charges and asymptotic symmetries in four dimensional conformal gravity I. Lovrekovic