Brane-Worlds and Higher Derivative Gravities

[eng] This thesis explores and combines, through the lens of the holographic correspondence, two relevant topics in the field of gravitational high-energy theory: higher-derivative theories of gravity and brane-world models. Part 1of the thesis deals with higher-derivative gravities. First, we focus on three-dimensional higher-curvature gravities. We present their equations of motion and study their spectrum when linearized around maximally symmetric spacetimes. We also identify all three-dimensional higher-curvature gravities satisfying a holographic c-theorem, and all three-dimensional Generalized Quasitopological Gravities. Then, we move on to the more general case of studying arbitrary higher-derivative gravities in spacetimes with any number of dimensions. We uncover the structure of their linearized equations in maximally symmetric spacetimes and describe their spectrum of gravitational perturbations in flat space. In Part 2, we introduce Karch-Randall brane-world models, in which a codimension-one brane sits near the boundary of an AdS bulk. We review and extend previously known results on the localization of gravity on the brane, both from the study of bulk metric perturbations, and from their reinterpretation through brane-world holography ---an effective higher-derivative theory of gravity coupled to a cut-off CFT on the brane. We then add a DGP term on the brane action and establish bounds for its coupling constant, beyond which the theory presents pathologies. Part 3 of the thesis draws from both previous topics and combines them to derive new results describing the properties of the induced gravity theory on the brane. First, we show how to calculate the higher-derivative terms of the induced theory, and we proceed to study it on its own, decoupling it from the cut-off CFT on the brane. We prove that, at each curvature order, the theory satisfies a holographic c-theorem. Finally, we study its linearization around flat space, taking into account the full series of higher-derivative terms. Besides the presence of the usual massless graviton, we uncover an infinite tower of massive spin-2 ghosts. Our findings shed light on brane-world holography and its applications as a model for semiclassical gravity within AdS/CFT.