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 × S 3 /Z m , where m is the NUT charge. Starting from a sixdimensional 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 /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.

The Swampland: Introduction and Review

“…We will see that it will also shed light on why Kaluza‐Klein modes happen to also satisfy the distance conjecture. This analysis is mostly based on unpublished work [], and we refer also to [] for relevant work on this topic.…”

Exact charges from heterotic black holes

“…, (4.2) where we denote the scalars collectively as φ i , with a ij some functions of the scalars 8 and F 2 (a) = F (a) µν F µν (a) . We are interested in finding solutions to the equations of motion derived from (4.2) describing the near-horizon region of an extremal black hole.…”

“…In order to make the comparison with previous literature transparent, the dimensional reduction of this section uses a different parametrization of the scalars than that of section 3.2 8. In the family of near-horizon solutions that we consider the scalars are constant, so the σ-model will play no role.…”

Black holes and (0,4) SCFTs from type IIB on K3

“…This was later extended to five-dimensional non-spinning black holes in M-theory on a Calabi-Yau threefold [2] and four-dimensional black holes in Mtheory on the product of a Calabi-Yau threefold with a circle by MSW [3]. More recently black holes in F-theory [4] have been given further consideration in [5][6][7] for example.In this paper we are interested in compactifications of type IIB string theory on K3 and the black strings emerging in this theory. The goal is to match macroscopic data with a complimentary microscopic description.…”

“…In this paper we compute the central charges and levels corresponding to the settings described above both from a macroscopic and microscopic viewpoint.Macroscopically we shall work exclusively in six-dimensional N = (2, 0) supergravity [9,10] which is obtained by compactifying type IIB on K3 [11]. The techniques for computing the various central charges and current algebra levels corresponding to the black string solutions of this theory were developed in [5,7,[12][13][14][15]. Concretely, we reduce the classical six-dimensional action to three dimensions in the black string background.…”