  The N_c to infinity limit of a matrix quantum field theory is equivalent to
summing only planar Feynman diagrams. The possibility of interpreting this sum
as some kind world-sheet theory has been in the air ever since 't Hooft's
original paper. We establish here just such a world sheet description for a
scalar quantum field with interaction term g\Tr\phi^3, and we indicate how the
approach might be extended to more general field theories.
