近日,美国康奈尔大学的Jeevan Chandra及其研究团队取得一项新进展。经过不懈努力,他们实现基于刘维尔线缺陷的三维黑洞统计。相关研究成果已于2024年11月14日在国际知名学术期刊《高能物理杂志》上发表。
该研究团队在三维引力中研究了这些解,并利用大c共形自举(conformal bootstrap)从对偶的共形场论(CFT)中再现了黑洞和虫洞的行为。创建薄壳黑洞的CFT算符是一种线缺陷,因此研究人员首先使用自举方法来研究线缺陷的统计量,既包括有限c的情况,也包括全息大c极限的情况。
交叉方程导出了在任何紧致、幺正的二维CFT(其中c > 1)中,线缺陷的高能矩阵元素的平均值的一个通用公式。其渐近行为由具有相同中心电荷值的Liouville CFT中的线缺陷所控制。
在大c情况下,三个不同的量是相互关联的:全息CFT中的线缺陷统计量、Liouville CFT中线缺陷的单个矩阵元素以及三维引力中黑洞和虫洞的在壳作用量。对于黑洞,这三种计算结果是匹配的,并且如果假设线缺陷的统计量近似为高斯分布,那么对偶CFT也可以再现一类虫洞。
据悉,在引力路径积分中,黑洞和虫洞可用于计算重算符的统计量。高维空间中的一个明显例子是由薄物质壳提供的。
附:英文原文
Title: Statistics of three-dimensional black holes from Liouville line defects
Author: Chandra, Jeevan, Hartman, Thomas, Meruliya, Viraj
Issue&Volume: 2024-11-14
Abstract: Black holes and wormholes in the gravitational path integral can be used to calculate the statistics of heavy operators. An explicit example in higher dimensions is provided by thin shells of matter. We study these solutions in 3D gravity, and reproduce the behavior of black holes and wormholes from the dual CFT using the large-c conformal bootstrap. The CFT operator that creates a thin shell black hole is a line defect, so we begin by using the bootstrap to study the statistics of line defects, both at finite c and in the holographic large-c limit. The crossing equation leads to a universal formula for the average high-energy matrix elements of the line defect in any compact, unitary 2d CFT with c > 1. The asymptotics are controlled by a line defect in Liouville CFT at the same value of the central charge. At large c, three distinct quantities are related: the statistics of line defects in holographic CFTs, the individual matrix elements of a line defect in Liouville CFT, and the on-shell action of black holes and wormholes in 3D gravity. The three calculations match for black holes, and if the statistics of the line defects are assumed to be approximately Gaussian, then a class of wormholes is also reproduced by the dual CFT.
DOI: 10.1007/JHEP11(2024)090
Source: https://link.springer.com/article/10.1007/JHEP11(2024)090