Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the “QFT data”: scaling dimensions of boundary operators, boundary Operator Product Expansion (OPE) coefficients and Boundary Operator Expansion (BOE)  coefficients for each bulk operator.  We 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, for simplicity in the case in which the bulk is two dimensional.

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. As such, they appear to be a promising non-perturbative tool to formulate predictions in weakly and strongly coupled QFTs.