Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data {∆i, Cijk, \( {b}_j^{\hat{\mathcal{O}}} \) }. These are the scaling dimensions of boundary operators ∆i, the boundary Operator Product Expansion (OPE) coefficients Cijk and the Boundary Operator Expansion (BOE) coefficients \( {b}_j^{\hat{\mathcal{O}}} \) 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.
