近日，印度数学科学研究所Sathiapalan, B.团队研究了从精确RG到平面空间全息RG的映射。该研究于2025年9月1日发表在《高能物理杂志》上。
此前研究给出了在边界上欧几里得CFT的欧几里得AdS空间中从第一性原理构造全息体对偶作用的方法。起点是边界理论的精确RG。从该ERG的演化算子获得大块动作，然后进行场重新定义。此过程保证边界相关器全部正确恢复。
研究组采用相同的方法，试图构造自由O(N)模型的全息对偶作用，其中体是平面边界壁的平坦欧几里得空间。结果发现标量三次相互作用是局部的（D = 3），但取决于与边界的距离——这可以解释为一个非恒定的背景膨胀场。研究组发现自旋2-标量-标量相互作用是非局域的，这与AdS的情况相反。
通过场的重新定义，研究组使动力学项在导数中成为四次项，可以消除这种非定域性。他们证明了通过规范固定一个具有线性化规范不变性与一般坐标不变性相关联的作用可以得到该作用。边界相关器（两点和三点）显示可以通过批量计算再现，正如这种全息方法所期望的那样。
附：英文原文
Title: Mapping from Exact RG to holographic RG in flat space
Author: Sathiapalan, B.
Issue&Volume: 2025-09-01
Abstract: In earlier papers a method was given for constructing from first principles a holographic bulk dual action in Euclidean AdS space for a Euclidean CFT on the boundary. The starting point was an Exact RG for the boundary theory. The bulk action is obtained from the evolution operator for this ERG followed by a field redefinition. This procedure guarantees that the boundary correlators are all recovered correctly. In this paper we use the same method in an attempt to construct a holographic dual action for the free O(N) model where the bulk is flat Euclidean space with a plane boundary wall. The scalar cubic interaction is found to be local (in D = 3) but depends on the distance from the boundary — which can be interpreted as a non constant background dilaton field. The spin 2-scalar-scalar interaction is found to be non local — in contrast to the AdS case. A field redefinition that makes the kinetic term quartic in derivatives can be done to eliminate this non locality. It is shown that the action can be obtained by gauge fixing an action that has the linearized gauge invariance associated with general coordinate invariance. Boundary correlators (two point and three point) are shown to be reproduced by bulk calculations — as expected in this approach to holography.
DOI: 10.1007/JHEP09(2025)022
Source: https://link.springer.com/article/10.1007/JHEP09(2025)022