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Quantum Field Theory (QFT) on hyperbolic space can be
characterized by a set of numbers that we call QFT data. 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.