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. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy’s formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy’s formula. We follow an effective field theory approach and consider the Kerr–Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.

我们仅使用引力和量子场论的工具，提出了 Kerr/CFT 对应关系及其扩展的主要结果的第一性原理推导。首先，我们回顾了极值黑洞的性质，特别是近视界极限内渐近维拉索罗对称性的构造。极值旋转或带电黑洞的熵与卡迪公式的手性一半相匹配。其次，我们展示了热二维共形场理论（CFT）如何与再现半经典极限中近极值黑洞周围的近超辐射探测器的动力学相关。第三，我们回顾了渐近平坦黑洞远离极值的隐藏共形对称性，并介绍了如何将非极值熵与卡迪公式相匹配。我们遵循有效的场论方法，并考虑克尔-纽曼黑洞及其在各种超引力理论中的推广。讨论了变形双共形场论对这些结果的解释，并与标准二维 CFT 的特性进行了对比。最后我们列出了一些未解决的问题。