New massive gravity extended with an arbitrary number of curvature corrections

We consider new massive gravity (NMG) type models in the context of AdS/CFT. By demanding the existence of a holographic $c$ theorem, we construct an infinite family of three-dimensional quantum gravity models, generalizing the NMG Lagrangian to arbitrarily high order in curvatures. We calculate the central charge $c$ and show that using Cardy’s formula it matches the entropy of black hole solutions. We also consider fluctuations about an anti-de Sitter background, finding ghostlike massive modes as in NMG. However, these can (a) be made massless by setting $c=0$, in which case these Lagrangians are expected to provide gravity duals for strongly coupled logarithmic conformal field theories, (b) be eliminated by imposing a single constraint on the parameters of the Lagrangian, thereby obtaining an infinite family of theories with the same perturbative content of three-dimensional general relativity.