Anomalies, black strings and the charged Cardy formula
Seyed Morteza Hosseini, Kiril Hristov, Yuji Tachikawa, Alberto Zaffaroni
Abstract
A bstract 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 AdS 5 × S 5 and AdS 7 × S 4 with horizon topology BTZt⋉ S 2 and BTZt⋉ S 2 × $$ {\Sigma}_{\mathfrak{g}} $$ <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> , respectively, where $$ {\Sigma}_{\mathfrak{g}} $$ <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> 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.