# Anomalous dimension of double-trace operators

Is it true that if a single-trace operator, say, $$O$$ acquires an anomalous dimension $$\gamma_o$$, then the anomalous dimension of the double-trace operator $$O^2$$ is $$2\gamma_o$$? If no, can anyone please provide counter-examples?

A correct statement is that in the large-N limit of a theory, if you have an operator $$O$$ with scaling dimension $$\Delta_O$$, the theory will also contain an operator $$O^2$$ with scaling dimension $$2\Delta_O$$.
2) If you include 1/N corrections the relation $$\Delta_{O^2} = 2 \Delta_O$$ won't be true anymore.