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. 
Federico Elmetti, Andrea Mauri, Silvia Penati, Alberto Santambrogio   and Daniela Zanon