  In this article we study the action of the one loop dilatation operator on
operators with a classical dimension of order N. These operators belong to the
su(2) sector and are constructed using two complex fields Y and Z. For these
operators non-planar diagrams contribute already at the leading order in N and
the planar and large N limits are distinct. The action of the one loop and the
two loop dilatation operator reduces to a set of decoupled oscillators and
factorizes into an action on the Z fields and an action on the Y fields. Direct
computation has shown that the action on the Y fields is the same at one and
two loops. In this article, using the su(2) symmetry algebra as well as
structural features of field theory, we give compelling evidence that the
factor in the dilatation operator that acts on the Ys is given by the one loop
expression, at any loop order.
