Rationality of the anomalous dimensions in N=4 SYM theory

We reconsider the general constraints on the perturbative anomalous dimensions in conformal invariant QFT and in particular in N=4 SYM with gauge group SU(N). We show that all the perturbative corrections to the anomalous dimension of a renormalized gauge invariant local operator can be written as polynomials in its one loop anomalous dimension. In the N=4 SYM theory the coefficients of these polynomials are rational functions of the number of colours N.