  We study a consistent deformation of the cubic open bosonic string theory in
such a way that the non-planar world sheet diagrams of the perturbative string
theory are mapped onto their equivalent planar diagrams of the light-cone
string field theory with some length parameters fixed. An explicit evaluation
of the cubic string vertex in the zero-slope limit yields the correct
relationship between the string coupling constant and the Yang-Mills coupling
constant. The deformed cubic open string field theory is shown to produce the
non-Abelian Yang-Mills action in the zero-slope limit if it is defined on
multiple D-branes. Applying the consistent deformation systematically to
multi-string world sheet diagrams, we may be able to calculate scattering
amplitudes with an arbitrary number of external open strings.
