  We derive the Wilson-Polchinski RG equation in the planar limit. We explain
that the equation necessarily involves also non-planar amplitudes with sphere
topology, which represent multi-trace contributions to the effective action.
The resulting RG equation turns out to be of the Hamilton-Jacobi type since
loop effects manifest themselves through terms which are linear in first order
derivatives of the effective action with respect to the sources. We briefly
outline applications to renormalization of non-commutative field theories,
matrix models with external sources and holography.
