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arXiv · 1808.05228

Four-dimensional black hole entropy from F-theory

Thomas W. Grimm·Huibert het Lam·Kilian Mayer·Stefan Vandoren
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Abstract

We study the central charges and levels of a two-dimensional $N=(0,4)$ superconformal field theory describing four-dimensional BPS black holes in F-theory. These arise from D3-branes wrapping a curve in the base of an elliptically fibered Calabi-Yau threefold times a circle, and probe a transverse Taub-NUT space. The near horizon geometry of these D3-branes is AdS$_3 \times \text{S}^3/\mathbb{Z}_m$, where $m$ is the NUT charge. Starting from a six-dimensional supergravity effective action we compute three-dimensional Chern-Simons terms to deduce the central charges and levels. We find that it is crucial to integrate out an infinite tower of massive Kaluza-Klein states on S$^3/\mathbb{Z}_m$ to match the expected microscopic results. The induced corrections turn out to contribute at leading order to the central charges and levels, which in turn determine the black hole entropy.

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Thomas W. Grimm, Huibert het Lam, Kilian Mayer, Stefan Vandoren. 2018-08-15. Four-dimensional black hole entropy from F-theory. https://doi.org/10.1007/jhep01(2019)037

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