Higher-curvature gravities from braneworlds and the holographic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math>-theorem
Pablo Bueno, Roberto Emparan, Quim Llorens
Abstract
We study the structure of the higher-curvature gravitational densities that are induced from holographic renormalization in ${\mathrm{AdS}}_{d+1}$. In a braneworld construction, such densities define a $d$-dimensional higher-curvature gravitational theory on the brane, which in turn is dual to a ($d\ensuremath{-}1$)-dimensional CFT living at its boundary. We show that this ${\mathrm{CFT}}_{d\ensuremath{-}1}$ 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.