arXiv 2210.014152022-10hep-thgr-qc

dS $_3$ / CFT $_2$对应中的后期关联函数

Late-time correlation functions in dS$_3$/CFT$_2$ correspondence

Heng-Yu Chen, Shi Chen, Yasuaki Hikida

备注：: 52 pages, 6 figures, minor changes, references added, to appear in JHEP
DOI：: 10.1007/JHEP02(2023)038

摘要：

本文在高自旋引力理论下计算了三维de Sitter时空的晚时关联函数。为此，我们详细阐述了从对偶共形场论中得到宇宙波泛函的公式，并将其用于计算后期的关联函数。我们认为，直接散装费曼图计算在制定的关系。此外，我们提供了一个精确的处方，以构建一个更高的自旋dS $_3$全息作为一个解析延续的Gaberdiel-Gopakumar对偶AdS $_3$。这里的部分结果已经在之前的一封信中报道过了。在本文中，我们解释了它们的推导细节，并将分析扩展到更一般的情况。在此之前，我们已经研究了两点和三点函数和一个简单的四点相关器在领先的牛顿常数。在这里，我们也评估更复杂的四点整流器。最后，我们研究了dS $_3$ /CFT $_2$在临界水平陪集的另一种极限下的后期相关器，如圆锥缺陷几何上的两点相关器。我们还研究了单回路校正dS $_3$上的两点相关器。

英文摘要：

We compute the late-time correlation functions on three-dimensional de Sitter spacetime for a higher-spin gravity theory. For this, we elaborate on the formulation to obtain the wave functional of universe from a dual conformal field theory, which is used to compute the late-time correlation functions. We argue that the relation to direct bulk Feynman diagram computations in the in-in formulation. We furthermore provide a precise prescription to construct a higher-spin dS$_3$ holography as an analytic continuation of Gaberdiel-Gopakumar duality for AdS$_3$. Part of results here were already reported in an earlier letter. We explain the details of their derivations and extend the analysis to more generic cases in this paper. Previously, we have examined two- and three-point functions and a simple four-point correlator at the leading order in Newton constant. Here we also evaluate more complicated four-point correlators. Finally, we study late-time correlators in an alternative limit of dS$_3$/CFT$_2$ with critical level coset, such as, two-point correlator on conical defect geometry. We also examine one-loop corrections to two-point correlator on dS$_3$.

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