Since in general one expects quantum-gravitational effects to induce corrections to the Einstein action, it is natural to consider modifying the gravitational part of the action with higher-derivative terms due to additional powers of the curvature. Such terms must be considered on the gravity side of the duality conjecture in order to study CFTs with different values for their central charges. Here, Lovelock gravity theories play a special role in that the number of metric derivatives in any field equation is never larger than 2. Furthermore, third-order Lovelock gravity is supersymmetric, and therefore one can define superconformal field theories via the AdS/CFT correspondence. The addition to the action of a term cubic in curvature is not new, but asymptotic Lifshitz solutions in Lovelock gravity coupled to a massive Abelian gauge field were only recently discovered.

A class of correction terms has been coined quasi-topological gravity, since in some ways they behave like topological invariants in 6 dimensions, yet for nonspherical geometries, they contribute nontrivially to the action. Furthermore, there are no Lagrangians that are cubic in curvature in four dimensions for spherical symmetry that lead to second order differential equations. Quasi-topological gravity has been previously studied in the case of planar AdS black holes.