# Is the leading order contribution to the double-trace operator anomalous dimension always $O(1/N^2)$?

Is the leading order contribution to the double-trace operator anomalous dimension always $$O(1/N^2)$$ ? I noticed that the double-trace contribution in Polchinski's paper hep-th/0907.0151 gets an anomalous dimension at $$O(1/N^2)$$. Is this true for any large-N CFT? If so, how to prove it? Are there counter-examples?