  We consider non-planar contributions to the correlation functions of BMN
operators in free N = 4 super Yang Mills theory. We recalculate these
non-planar contributions from a different kind of diagram and find some exact
agreements. The vertices of these diagrams are represented by free planar three
point functions, thus our calculations provide some interesting identities for
correlation functions of BMN operators in N = 4 super Yang Mills theory. These
diagrams look very much like loop diagrams in a second quantized string field
theory, thus these identities could possibly be interpreted as natural
consequences of the pp-wave/CFT correspondence.
