In this paper an Exact Renormalization Group (ERG) equation is written for 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 Sathiapalan and Sonoda (2017) [1] 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 $Ad{S}_{D+1}$ using the techniques of ([1]). 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.

在本文中，针对临界点编写了一个精确的重新规范化组（ERG）方程 $Ø（ñ）$D维模型（带有$d\approx 3$）在标量复合算子扰动的Wilson-Fisher定点处。该动作是根据辅助标量字段编写的，并再现了标量复合算符的相关函数。该方程是从基本标量场的Polchinski ERG方程出发得出的。如Sathiapalan和Sonoda（2017）所述[1]，Polchinski ERG方程的演化算子可以用函数积分的形式写成，其中$d+\mathrm{1个}$维标量场理论作用。在基本标量场的情况下，该动作仅具有动力学项，因此看起来与具有潜在项的Holographic RG完全不同。但是，在本文讨论的复合算子情况下，ERG方程，因此$d+\mathrm{1个}$三维作用包含标量场的高阶势项，因此与全息RG的情况非常相似。此外，该动作可以映射到标量字段动作中$\mathrm{一种}d{\mathrm{小号}}_{d+\mathrm{1个}}$使用（[1]）的技术。本文计算了势的前立方项$d\approx 3$ 并有望消失 $d=3$ 与AdS / CFT文献中的结果一致。