Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data \lbrace \Delta_i,C_{ijk},b^{\hat{\mathcal{O}}}_j\rbrace. These are the scaling dimensions of boundary operators \Delta_i, the boundary Operator Product Expansion (OPE) coefficients C_{ijk} and the Boundary Operator Expansion (BOE) coefficients b^{\hat{\mathcal{O}}}_j that characterize how each bulk operator \hat{\mathcal{O}} can be expanded in terms of boundary operators \mathcal{O}_j. For simplicity, we focus on two dimensional QFTs and derive a universal set of first order Ordinary Differential Equations (ODEs) that encode the variation of the QFT data under an infinitesimal change of a bulk relevant coupling. In principle, our ODEs can be used to follow a Renormalization Group (RG) flow starting from a solvable QFT into a strongly coupled phase and to the flat space limit.
