论文标题
来自精确RG的散装量规场和全息RG
Bulk Gauge Fields and Holographic RG from Exact RG
论文作者
论文摘要
最近，描述了一种方法是从$ ads_ {d+1} $空间中从$ d $二维边界CFT的精确rg方程开始的方法（Sathiapalan，Sonoda，2017年）。与精确RG方程相对应的进化运算符被重写为$ d+1 $ dimensional字段理论的功能积分，$ ads_ {d+1} $ space。此后，该方法已应用于$ O（N）$模型中的基本标量和复合标量（Sathiapalan，2020）。在本文中，我们将此技术应用于保守的向量电流和边界CFT的能量动量张量，即固定点的$ O（n）$模型。这些复合旋转的一个和自旋两个操作员由辅助场表示，并以仪表场和度量扰动的形式延伸到整体中。我们在自由级别获得（固定的）麦克斯韦和爱因斯坦的作用。尽管所涉及的步骤是由AD/CFT对应的激励，但在逻辑上，没有任何步骤需要ADS/CFT猜想才能证明其理由。
Recently, a method was described for deriving Holographic RG equation in $AdS_{D+1}$ space starting from an Exact RG equation of a $D$-dimensional boundary CFT (Sathiapalan, Sonoda, 2017). The evolution operator corresponding to the Exact RG equation was rewritten as a functional integral of a $D+1$ dimensional field theory in $AdS_{D+1}$ space. This method has since been applied to elementary scalars and composite scalars in the $O(N)$ model (Sathiapalan, 2020). In this paper, we apply this technique to the conserved vector current and the energy momentum tensor of a boundary CFT, the $O(N)$ model at a fixed point. These composite spin one and spin two operators are represented by auxiliary fields and extend into the bulk as gauge fields and metric perturbations. We obtain, at the free level, the (gauge fixed) Maxwell and Einstein actions. While the steps involved are motivated by the AdS/CFT correspondence, none of the steps logically require the AdS/CFT conjecture for their justification.
