Four-dimensional black hole entropy from F-theory

Thomas W. Grimm; Huibert het Lam; Kilian Mayer; Stefan Vandoren

doi:10.1007/JHEP01(2019)037

Four-dimensional black hole entropy from F-theory

Thomas W. Grimm, Huibert het Lam, Kilian Mayer, Stefan Vandoren

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Journal	Journal of High Energy Physics
Volume	37
DOIs	https://doi.org/10.1007/JHEP01(2019)037
Publication status	Published - 4 Jan 2019

Keywords

Black Holes in String Theory
conformal field theory
F-theory

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title = "Four-dimensional black hole entropy from F-theory",

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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AU - Lam, Huibert het

AU - Mayer, Kilian

AU - Vandoren, Stefan

N1 - 44 pages; v2: minor typos corrected

PY - 2019/1/4

Y1 - 2019/1/4

N2 - 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.

AB - 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.

KW - Black Holes in String Theory

KW - conformal field theory

KW - F-theory

U2 - 10.1007/JHEP01(2019)037

DO - 10.1007/JHEP01(2019)037

M3 - Article

SN - 1029-8479

VL - 37

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

ER -

Four-dimensional black hole entropy from F-theory

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Keywords

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