  The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena
conjecture to a new regimen of direct tests. In one line of pursuit,
finite-radius curvature corrections to the Penrose limit (which appear in
inverse powers of the string angular momentum J) have been found to induce a
complicated system of interaction perturbations to string theory on the
pp-wave; these have been successfully matched to corresponding corrections to
the BMN dimensions of N=4 super Yang-Mills (SYM) operators to two loops in the
't Hooft coupling lambda. This result is tempered by a well-established
breakdown in the correspondence at three loops. Notwithstanding the third-order
mismatch, we proceed with this line of investigation by subjecting the string
and gauge theories to new and significantly more rigorous tests. Specifically,
we extend our earlier results at O(1/J) in the curvature expansion to include
string states and SYM operators with three worldsheet or R-charge impurities.
In accordance with the two-impurity problem, we find a perfect and intricate
agreement between both sides of the correspondence to two-loop order in lambda
and, once again, the string and gauge theory predictions fail to agree at third
order.
