New results in the deformed N=4 SYM theory

We investigate various perturbative properties of the deformed N=4 SYM theory. We carry out a three-loops calculation of the chiral matter superfield propagator and derive the condition on the couplings for maintaining finiteness at this order. We compute the 2-, 3- and 4-point functions of composite operators of dimension 2 at two loops. We identify all the scalar operators (chiral and non-chiral) of bare dimension 4 with vanishing one-loop anomalous dimension. We compute some 2- and 3-point functions of these operators at two loops and argue that the observed finite corrections cannot be absorbed by a finite renormalization of the operators.