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arXiv · 1912.00029

On the exact entropy of $\mathcal{N}=2$ black holes

João Gomes·Huibert het Lam·Grégoire Mathys
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Abstract

We study the exact entropy of four-dimensional $\mathcal{N}=2$ black holes in M-theory both from the brane and supergravity points of view. On the microscopic side the degeneracy is given by a Fourier coefficient of the elliptic genus of the dual two-dimensional $\mathcal{N}=(0,4)$ SCFT and can be extracted via a Rademacher expansion. We show how this expansion is mapped to a modified OSV formula derived by Denef and Moore. On the macroscopic side the degeneracy is computed by applying localization techniques to Sen's quantum entropy functional reducing it to a finite number of integrals. The measure for this finite dimensional integral is determined using a connection with Chern-Simons theory on AdS$_2 \times$S$^1$. The leading answer is a Bessel function in agreement with the microscopic answer. Other subleading corrections can be explained in terms of instanton contributions.

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João Gomes, Huibert het Lam, Grégoire Mathys. 2019-11-29. On the exact entropy of $\mathcal{N}=2$ black holes. https://arxiv.org/abs/1912.00029

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