We derive the general anomaly polynomial for a class of two-dimensional CFTs arising as twisted compactifications of a higher-dimensional theory on compact manifolds ℳd, including the contribution of the isometries of ℳd. We then use the result to per- form a counting of microstates for electrically charged and rotating supersymmetric black strings in AdS5 × S5 and AdS7 × S4 with horizon topology BTZt⋉S2 and BTZt⋉S2 × $$ {\Sigma}_{\mathfrak{g}} $$ , respectively, where $$ {\Sigma}_{\mathfrak{g}} $$ is a Riemann surface. We explicitly construct the latter class of solutions by uplifting a class of four-dimensional rotating black holes. We provide a microscopic explanation of the entropy of such black holes by using a charged version of the Cardy formula.

中文翻译：

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异常、黑线和带电的 Cardy 公式

我们推导出了一类二维 CFT 的一般异常多项式，它是对紧流形 ℳd 的高维理论的扭曲紧缩，包括 ℳd 的等距的贡献。然后，我们使用该结果对具有水平拓扑 BTZt⋉S2 和 BTZt⋉S2 × $$ {\Sigma}_{\mathfrak 的 AdS5 × S5 和 AdS7 × S4 中带电和旋转的超对称黑色弦进行微观状态计数{g}} $$ ，其中 $$ {\Sigma}_{\mathfrak{g}} $$ 是黎曼曲面。我们通过提升一类四维旋转黑洞来明确构建后一类解决方案。我们通过使用卡迪公式的带电版本对此类黑洞的熵进行了微观解释。