Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real

We study the cal{N}=1 SU(N) SYM theory which is a marginal deformation of the cal{N}=4 theory, with a complex deformation parameter beta. We consider the large N limit and study perturbatively the conformal invariance condition. We find that finiteness requires reality of the deformation parameter beta.