  Correlation functions in perturbative N=4 supersymmetric Yang-Mills theory
are examined in the Berenstein-Maldacena-Nastase (BMN) limit. We demonstrate
that non-extremal four-point functions of chiral primary fields are ill-defined
in that limit. This lends support to the assertion that only gauge theoretic
two-point functions should be compared to pp-wave strings. We further refine
the analysis of the recently discovered non-planar corrections to the planar
BMN limit. In particular, a full resolution to the genus one operator mixing
problem is presented, leading to modifications in the map between BMN operators
and string states. We give a perturbative construction of the correct operators
and we identify their anomalous dimensions. We also distinguish symmetric,
antisymmetric and singlet operators and find, interestingly, the same torus
anomalous dimension for all three. Finally, it is discussed how operator mixing
effects modify three point functions at the classical level and, at one loop,
allow us to recover conformal invariance.
