From Euclidean sources to Lorentzian spacetimes in holographic conformal field theories
From Euclidean sources to Lorentzian spacetimes in holographic conformal field theories
复制标题
从欧几里得源到全息共形场论中的洛伦兹时空
DOI：
--
复制
发表时间：
2017
影响因子：
5.4
通讯作者：
M. Raamsdonk
中科院分区：
文献类型：
--
作者：
D. Marolf;Onkar Parrikar;Charles Rabideau;A. Rad;M. Raamsdonk
我们认为全息共形场理论的状态，通过添加本地运营商的欧几里德路径积分的来源，调查的目的是在何种程度上可以表示任意散装相干态的这种欧几里德路径积分的CFT。我们在源中微扰地构造了相应的对偶洛伦兹时空。推广了以前的工作，我们给出了任意维一般标量场和度规扰动源中一阶洛伦兹场的显式公式。我们检查的结果，通过全息计算的洛伦兹一点函数的源操作员和比较与直接CFT计算。我们提出的证据表明，在线性化的水平，任意批量的初始数据配置文件可以产生适当的选择欧几里德来源。然而，为了产生非常局部化的初始数据，振幅必须同时取小，否则所需的源发散，使微扰方法无效。
We consider states of holographic conformal field theories constructed by adding sources for local operators in the Euclidean path integral, with the aim of investigating the extent to which arbitrary bulk coherent states can be represented by such Euclidean path-integrals in the CFT. We construct the associated dual Lorentzian spacetimes perturbatively in the sources. Extending earlier work, we provide explicit formulae for the Lorentzian fields to first order in the sources for general scalar field and metric perturbations in arbitrary dimensions. We check the results by holographically computing the Lorentzian one-point functions for the sourced operators and comparing with a direct CFT calculation. We present evidence that at the linearized level, arbitrary bulk initial data profiles can be generated by an appropriate choice of Euclidean sources. However, in order to produce initial data that is very localized, the amplitude must be taken small at the same time otherwise the required sources diverge, invalidating the perturbative approach.