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arXiv 2408.00628hep-th
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从精确重整化群到平直空间中的全息重整化群

Mapping from Exact RG to Holographic RG in Flat Space

B. Sathiapalan

备注：
23 pages. Revised version to be published in JHEP. The scalar-scalar-graviton bulk vertex is shown in the revised version to be local after a field redefinition involving the graviton. Some more computational details have been provided in an Appendix
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AI总结：

本文利用精确重整化群方法，在平直空间带平面边界墙的背景下为自由O(N)模型构造全息对偶作用量，发现标量三次相互作用局域但依赖边界距离，并通过场重定义消除非局域性，最终重现边界关联函数。

摘要：

在早前的论文中，给出了一种方法，从第一性原理出发，为边界上的欧几里得共形场论（CFT）在欧几里得反德西特（AdS）空间中构造全息体态对偶作用量。其出发点是边界理论的精确重整化群（ERG）。体态作用量由该ERG的演化算符经过场重定义后得到。这一过程保证了边界关联函数都能被正确恢复。在本文中，我们使用相同的方法尝试为自由$O(N)$模型构造全息对偶作用量，其中体态为具有平面边界墙的欧几里得平直空间。发现标量三次相互作用是局域的（在$D=3$时），但依赖于距边界的距离——这可以解释为非恒定的背景膨胀子场。发现自旋2-标量-标量相互作用是非局域的——与AdS情形形成对比。可以进行一个使动能项在导数上变为四次的场重定义，以消除这种非局域性。文中证明了该作用量可以通过对具有与一般坐标不变性相关的线性化规范不变性的作用量进行规范固定而获得。边界关联函数（两点和三点）被证明可以由体态计算重现——正如在全息方法中所预期的那样。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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