  We study correlation functions of the bulk stress tensor and boundary
operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In
particular, we derive new sum rules from the two-point function of the stress
tensor and its three-point function with two boundary operators. In AdS2, this
leads to a bootstrap setup that involves the central charge of the UV limit of
the bulk QFT and may allow us to follow a Renormalization Group (RG) flow
non-perturbatively by continuously varying the AdS radius. Along the way, we
establish the convergence properties of the newly discovered local block
decomposition of the three-point function.
