  It was recently shown, using the AdS/CFT correspondence, that the low energy
effective action of a large $N$ open string theory satisfies a holographic RG
flow equation closely related to the Hamilton-Jacobi equation of 5-d
supergravity. In this paper we re-obtain the same flow equation in the dual
regime of small 't Hooft coupling $\lambda\ll 1$. Our derivation makes use of
the conformal equivalence between planar open string diagrams and closed string
tree diagrams. This equivalence can be viewed as a microscopic explanation of
the open/closed string duality that underlies the AdS/CFT correspondence.
