Anomalies, black strings and the charged Cardy formula

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<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>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<jats:sub><jats:italic>d</jats:italic></jats:sub>, including the contribution of the isometries of ℳ<jats:sub><jats:italic>d</jats:italic></jats:sub>. We then use the result to per- form a counting of microstates for electrically charged and rotating supersymmetric black strings in AdS<jats:sub>5</jats:sub><jats:italic>× S</jats:italic><jats:sup>5</jats:sup> and AdS<jats:sub>7</jats:sub><jats:italic>× S</jats:italic><jats:sup>4</jats:sup> with horizon topology BTZt⋉<jats:italic>S</jats:italic><jats:sup>2</jats:sup> and BTZt⋉<jats:italic>S</jats:italic><jats:sup>2</jats:sup><jats:italic>×</jats:italic><jats:inline-formula><jats:alternatives><jats:tex-math>$$ {\Sigma}_{\mathfrak{g}} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, respectively, where <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {\Sigma}_{\mathfrak{g}} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> 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.</jats:p>

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