Anomalies, Black strings and the charged Cardy formula

TL;DR

This paper derives anomaly polynomials for 2D CFTs from higher-dimensional theories, applies them to count microstates of supersymmetric black strings in AdS spaces, and explains their entropy via a charged Cardy formula.

Contribution

It introduces a general method to compute anomaly polynomials for twisted compactifications and uses this to microstate count and entropy explanation for specific black string solutions.

Findings

Derived anomaly polynomial for 2D CFTs from higher-dimensional theories.

Counted microstates of supersymmetric black strings in AdS spaces.

Provided a microscopic entropy explanation using a charged Cardy formula.

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 $\mathcal{M}_d$, including the contribution of the isometries of $\mathcal{M}_d$. We then use the result to perform a counting of microstates for electrically charged and rotating supersymmetric black strings in AdS$_5\times S^5$ and AdS$_7\times S^4$ with horizon topology BTZ$ \ltimes S^2$ and BTZ$ \ltimes S^2 \times \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.