Anomalies, black strings and the charged Cardy formula

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×$$ {\Sigma}_{\mathfrak{g}} $$ Σ g , respectively, where $$ {\Sigma}_{\mathfrak{g}} $$ Σ 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.