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Holographic model of massive scalar field with its self-interaction$\lambda\phi^n$ in AdS space is able to give a logarithmic scale dependence tomarginal multi trace deformation couplings on its dual conformal field theory,where $\lambda$ is the self-interaction coupling of the scalar field, $\phi$and $n$ is an integral number. In arXiv:1501.06664, the authors realize thisfeature by looking at bulk scalar solutions near AdS boundary imposing aspecific boundary condition between the coefficients of non-normalizable andnormalizable modes of the scalar field excitations. We study the sameholographic model to see scale dependence of marginal deformations on the dualconformal field theory by employing completely different method: {\itholographic Wilsonian renormalization group}. We solve Hamilton-Jacobi equationderived from the holographic model of massive scalar with $\lambda\phi^n$interaction and obtain the solution of marginal multi trace deformations up tothe leading order in $\lambda$. It turns out that the solution of marginalmulti trace deformation also presents logarithmic behavior in energy scale nearUV region.

On holographic Wilsonian renormalization group of massive scalar theory with its self-interactions in AdS