On the many facets of the AdS/CFT correspondence – from bootstrap to supergravity - Ferrero, P (2022)
In this thesis we consider two distinct approaches to the study of the AdS/CFT correspondence. In the first we study correlation functions of local operators in holographic SCFTs, which from the bulk perspective represent the most natural generalization of flat-space scattering amplitudes to AdS backgrounds. For maximally supersymmetric CFTs, all four-point functions between single-trace half-BPS operators have been recently computed at tree level, using the idea of maximally R-symmetry violating (MRV) limit. In this thesis we illustrate how the MRV limit can be used to derive analogous results in theories with less than maximal supersymmetry, where the external operators that we consider are dual to gluons in AdS. We analyze our results in detail, finding several interesting features of (super) gluon scattering amplitudes in AdS, ranging from color-kinematics duality to Parisi-Sourlas supersymmetry and hidden conformal symmetry. We also revisit the results for maximally supersymmetric theories, where the half-BPS operators are dual to gravitons, in particular examining certain properties related to dimensional reductions: the existence of protected sectors and again Parisi-Sourlas supersymmetry.