Critical theories of gravity are certain higher derivative theories in which parameters are so tuned as to eliminate massive excitations for the spin-2 field. Asymptotically AdS black hole entropy in these theories works out to be zero. We show that such theories arise naturally on the boundary of AdS in the form of counterterms. Such counterterms are derived by demanding cutoff independence of the Euclidean onshell action and black hole entropy.
The resummed higher derivative action so obtained can be shown to be critical. Connections with log-CFTs will be discussed. For a specific choice of parameters, these theories turn out to be non-dynamical.