Renormalized AdS action and Critical Gravity
  It is shown that the renormalized action for AdS gravity in even spacetime dimensions is equivalent -on shell- to a polynomial of the Weyl tensor, whose first non-vanishing term is proportional to $Weyl^2$. Remarkably enough, the coupling of this last term coincides with the one that appears in Critical Gravity. 
Olivera Miskovic, Rodrigo Olea and Minas Tsoukalas
hep-th gr-qc