Abstract: 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.
First, we study arbitrary higher-derivative gravities in D-dimensional spacetimes, uncovering the structure of their linearized equations in maximally symmetric spacetimes and their corresponding spectrum.
Next, we introduce Karch-Randall brane-world models, in which a codimension-one brane sits near the boundary of an AdS bulk. We extend previously known results on the localization of gravity on the brane. We add a DGP term on the brane action and establish bounds for its coupling constant.
Finally, we combine both previous topics to derive new results on the induced higher-derivative theory of gravity on the brane. We prove that it satisfies a holographic c-theorem, and we study its linearization around Minkowski space.
Our findings shed light on brane-world holography and its applications as a model for semiclassical gravity within AdS/CFT.

Supervisors: Roberto Emparan and Pablo Bueno