  We show that the gamma_i-deformation, which was proposed as candidate gauge
theory for a non-supersymmetric three-parameter deformation of the AdS/CFT
correspondence, is not conformally invariant due to a running double-trace
coupling - not even in the 't Hooft limit. Moreover, this non-conformality
cannot be cured when we extend the theory by adding at tree-level arbitrary
multi-trace couplings that obey certain minimal consistency requirements. Our
findings suggest a possible connection between this breakdown of conformal
invariance and a puzzling divergence recently encountered in the
integrability-based descriptions of two-loop finite-size corrections for the
single-trace operator of two identical chiral fields. We propose a test to
clarify this.
