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

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