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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 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.
Highlights
The charged Cardy formula, c c J2 log ρ(n, J) ≈ 2π n− −, (1.1)gives the asymptotic density of states ρ(n, J) of a 2d conformal field theory (CFT) with a U(1) symmetry of level k in a sector with a given U(1) charge
The black hole carries n units of momentum along the circle, and its entropy perfectly matches the charged Cardy formula using the levels for flavor and rotational symmetry predicted by the integration of the anomaly polynomial of the six-dimensional (2, 0) theory
It would be interesting to give an independent derivation of the charged Cardy formula from the refined topologically twisted index of N = 2 super Yang-Mills (SYM) in five dimensions [37],21 which is supposed to reproduce the elliptic genus of the 2d CFT
Summary
Gives the asymptotic density of states ρ(n, J) of a 2d conformal field theory (CFT) with a U(1) symmetry of level k in a sector with a given U(1) charge. We consider asymptotically AdS7 × S4 supersymmetric black strings, corresponding to the compactification of the (2, 0) theory on S2 × Σg, and carrying charge under the Cartan subgroup of the SO(5) R-symmetry in six dimensions and rotating along S2 We explicitly construct their near-horizon horizon geometry, which has topology BTZ S2 × Σg, using a generalization of the methods introduced in [22]. The black hole carries n units of momentum along the circle, and its entropy perfectly matches the charged Cardy formula using the levels for flavor and rotational symmetry predicted by the integration of the anomaly polynomial of the six-dimensional (2, 0) theory. In the appendix we rephrase our supergravity findings in the language of attractors and entropy functions, using the gravitational blocks introduced in [25]
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