Central functions and their physical implications

Central functions c(g) and c'(g) are constructed in quantum field theory. These quantities justify and generalize the notions of central charges recently introduced at criticality, which, together with suitable anomalous dimensions h, identify a conformal field theory in four dimensions (CFT4). They are encoded in the four-point function of the stress-energy tensors. The behavior of the central functions is analysed to two-loops in perturbation theory. The central function is the fundamental notion for a description of quantum field theory as a radiative interpolation between pairs of CFT4's. The problem of computating their RG flow in the far IR limit starting from the UV fixed point is addressed in the context of supersymmetric gauge theories and electric-magnetic duality