  In this article we compute the anomalous dimensions for a class of operators,
belonging to the SU(3) sector of the theory, that have a bare dimension of
order N. For these operators the large N limit and the planar limit are
distinct and summing only the planar diagrams will not capture the large N
dynamics. Although the spectrum of anomalous dimensions has been computed for
this class of operators, previous studies have neglected certain terms which
were argued to be small. After dropping these terms diagonalizing the
dilatation operator reduces to diagonalizing a set of decoupled oscillators. In
this article we explicitly compute the terms which were neglected previously
and show that diagonalizing the dilatation operator still reduces to
diagonalizing a set of decoupled oscillators.
