论文标题
O（n）模型中的全息RG和精确的RG
Holographic RG and Exact RG in O(N) Model
论文作者
论文摘要
在本文中，在Wilson-Fisher固定点上，为$ D $ Dimensions（$ d $ Dimensions（$ d \ 3 $）中的关键$ O（N）$模型编写了一个精确的重归其化组（ERG）方程。该动作是根据辅助标量字段编写的，并重现标量复合算子的相关函数。该方程式从基本标量场的Polchinski ERG方程开始。如Arxiv中所述：1706.03371 Polchinski ERG方程的进化运算符可以以功能积分的形式编写，并具有$ d+1 $ dimensional Scalion calistr Field Theory Compation。在基本标量字段的情况下，该动作只有一个动力学项，因此与有潜在术语的全息RG看起来完全不同。但是，在本文讨论的复合操作员情况下，ERG方程和$ d+1 $尺寸动作包含标量场的高阶潜在项，因此与全息RG的情况非常相似。此外，使用Arxiv的技术：1706.03371，可以将此动作映射到$ ads_ {D+1} $中的标量现场操作。本文以$ d \ 3 $计算了潜力的主要立方术语，预计在$ d = 3 $中消失了与广告/CFT文献中的结果一致。
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.
