13869 2006.08629 10.1007/JHEP09(2020)167 167 167 Anomalies, black strings and the charged Cardy formula 01 Mathematical Sciences 0101 Pure Mathematics Regular Article - Theoretical Physics 1 41 2020 9 25 2020 7 14 2020 9 1 2020 9 25 The Author(s) 2020 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2020 2020 9 9 Seyed Morteza Hosseini morteza.hosseini@ipmu.jp Kiril Hristov khristov@inrne.bas.bg Yuji Tachikawa yuji.tachikawa@ipmu.jp Alberto Zaffaroni alberto.zaffaroni@mib.infn.it grid.26999.3d 0000 0001 2151 536X Kavli IPMU (WPI), UTIAS The University of Tokyo Kashiwa Chiba 277-8583 Japan grid.410344.6 0000 0001 2097 3094 Institute for Nuclear Research and Nuclear Energy Bulgarian Academy of Sciences Tsarigradsko Chaussee 72 1784 Sofia Bulgaria grid.7563.7 0000 0001 2174 1754 Dipartimento di Fisica Università di Milano-Bicocca I-20126 Milano Italy NFN, sezione di Milano-Bicocca I-20126 Milano Italy Abstract 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 ℳ d , including the contribution of the isometries of ℳ d . We then use the result to per- form a counting of microstates for electrically charged and rotating supersymmetric black strings in AdS5 × S 5 and AdS7 × S 4 with horizon topology BTZt⋉S 2 and BTZt⋉S 2 × Σ g $$ {\Sigma}_{\mathfrak{g}} $$ , respectively, where Σ g $$ {\Sigma}_{\mathfrak{g}} $$ 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. Keywords AdS-CFT Correspondence Anomalies in Field and String Theories Black Holes in String Theory Field Theories in Higher Dimensions ArXiv ePrint: 2006.08629