  I define central functions c(g) and c'(g) in quantum field theory, useful to
study the flow of the numbers of vector, spinor and scalar degrees of freedom
from the UV limit to the IR limit and basic ingredients for a description of
quantum field theory as an interpolating theory between pairs of 4D conformal
field theories. The key importance of the correlator of four stress-energy
tensors is outlined in this respect. Then I focus the analysis on the
behaviours of the central functions in QCD, computing their slopes in the UV
critical point. To two-loops, c(g) and c'(g) point towards the expected IR
directions. As a possible physical application, I argue that a closer study of
the central functions might allow us to lower the upper bound on the number of
generations to the observed value. Candidate all-order expressions for the
central functions are compared with the predictions of electric-magnetic
duality.
