  In the large N limit of N=4 Super Yang-Mills, the mixing under dilatations of
the SU(2) sector, single trace operators composed of L complex scalar fields of
two types, is closed to all orders in perturbation theory. By relying on the
AdS/CFT correspondence, and by examining the currents for semiclassical
strings, we present evidence which implies that there are small mixings that
contradict the closure of the SU(2) sector in the strong coupling limit. These
mixings first appear to second order in the \lambda/L^2 expansion.
