I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimension equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS\(_4\) black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS\(_5\) black holes.

中文翻译：

---

AdS 黑洞、全息术和定位

我回顾了使用全息术计算维度等于或大于 4 的 AdS 超对称黑洞微观状态数量的一些最新进展。通过将定位和矩阵模型技术应用于对偶场理论来获得计数。我详细介绍了动态 AdS \(_4\)黑洞的情况，对应于双场理论的扭曲紧致化，并讨论了旋转 AdS \(_5\)黑洞的最新技术。