QFT as a set of ODEs

Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data. These are the scaling dimensions of boundary operators, the boundary Operator Product Expansion (OPE) coefficients and the Boundary Operator Expansion (BOE) coefficients that characterize how each bulk operator can be expanded in terms of boundary operators. 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 flow starting from a solvable QFT into a strongly coupled phase and to the flat space limit.