  In this paper an Exact Renormalization Group (ERG) equation is written for
the the critical $O(N)$ model in $D$-dimensions (with $D\approx 3$) at the
Wilson-Fisher fixed point perturbed by a scalar composite operator. The action
is written in terms of an auxiliary scalar field and reproduces correlation
functions of a scalar composite operator. The equation is derived starting from
the Polchinski ERG equation for the fundamental scalar field. As described in
arXiv:1706.03371 an evolution operator for the Polchinski ERG equation can be
written in the form of a functional integral, with a $D+1$ dimensional scalar
field theory action. In the case of the fundamental scalar field this action
only has a kinetic term and therefore looks quite different from Holographic RG
where there are potential terms. But in the composite operator case discussed
in this paper, the ERG equation and consequently the $D+1$ dimensional action
contains higher order potential terms for the scalar field and is therefore
very similar to the case of Holographic RG. Furthermore this action can be
mapped to a scalar field action in $AdS_{D+1}$ using the techniques of
arXiv:1706.03371. The leading cubic term of the potential is computed in this
paper for $D \approx 3$ and expectedly vanishes in $D=3$ in agreement with
results in the AdS/CFT literature.
