  Using the coherent state formalism we calculate matrix elements of the
one-loop non-planar dilatation operator of ${\cal N}=4$ SYM between operators
dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior.
We comment on the {\it qualitative} similarity of our matrix elements to the
interaction vertex of a string field theory. In addition, we present a solvable
toy model for string splitting and joining. The scaling behaviour of the matrix
elements suggests that the contribution to the genus one energy shift coming
from semi-classical string splitting and joining is small.
