The Kerr/CFT Correspondence and its Extensions.
The Kerr/CFT Correspondence and its Extensions.
复制标题
Kerr/CFT对应关系及其扩展。
DOI：
10.12942/lrr-2012-11
复制
发表时间：
2012
影响因子：
40.6
通讯作者：
Compère G
中科院分区：
文献类型：
--
作者：
Compère G
我们仅使用引力和量子场论的工具，对 Kerr/CFT 对应的主要结果及其扩展进行了第一性原理推导，在必要时填补了文献中的一些空白。首先，我们回顾了极值黑洞的性质，根据半经典量子化规则，这些性质意味着它们的近视界量子态形成一维共形群的中心扩展表示。这引发了这样的猜想：极值克尔黑洞和赖斯纳-诺德斯特伦黑洞对于二维 CFT 的手性极限是对偶的。我们还提出了 SL(2, ℤ) 系列二维 CFT 的存在，这些二维 CFT 描述了极值克尔-纽曼黑洞的手性极限。我们提出反德西特时空的概括，并讨论其他物质耦合和高导数修正。其次，我们展示了这些 CFT 的近手性极限如何在半经典极限中重现近极值黑洞周围的近超辐射探测器的动力学。第三，我们回顾了远离极值的渐近平坦黑洞隐藏的共角对称性，结合它们在极值处的特性，如何能够对非极值渐近平坦旋转或带电黑洞的熵进行微观解释。最后我们列出了一些未解决的问题。
We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordström black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL(2, ℤ) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.