Higher-curvature Gravities from Braneworlds and the Holographic c-theorem

We study the structure of the higher-curvature gravitational densities that are induced from holographic renormalization in AdS$_{d+1}$. In a braneworld construction, such densities define a d-dimensional higher-curvature gravitational theory on the brane, which in turn is dual to a (d-1)-dimensional CFT living at its boundary. We show that this CFT$_{d-1}$ satisfies a holographic c-theorem in general dimensions (different than the g-theorem of holographic boundary CFTs), since at each and every order the higher-curvature densities satisfy c-theorems on their own. We find that, in these densities, the terms that affect the monotonicity of the holographic c-function are algebraic in the curvature, and do not involve covariant derivatives of the Riemann tensor. We examine various other features of the holographically induced higher-curvature densities, such as the presence of reduced-order traced equations, and their connection to Born-Infeld-type gravitational Lagrangians.