Four-dimensional black hole entropy from F-theory

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

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Four-dimensional black hole entropy from F-theory

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

High Energy Physics - Theory · Submitted 15 Aug 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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arXiv ID1808.05228 (version 2)

Pith IDM5TNXNCP, Pith's permanent record of this paper and its review

CitationHuibert het Lam, Kilian Mayer, Stefan Vandoren, Thomas W. Grimm. "Four-dimensional black hole entropy from F-theory." arXiv:1808.05228 (2018). https://pith.science/paper/M5TNXNCP

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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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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 1.00	0.91	0.08	asserted 0.95
s1	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.	background 0.50	0.21	0.03	asserted 1.00
s2	The near horizon geometry of these D3-branes is AdS$_3 \times \text{S}^3/\mathbb{Z}_m$, where $m$ is the NUT charge.	background 0.67	0.24	0.05	asserted 1.00
s3	Starting from a six-dimensional supergravity effective action we compute three-dimensional Chern-Simons terms to deduce the central charges and levels.	method 0.99	0.95	0.06	asserted 1.00
s4	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.	result 0.79	0.93	0.40	asserted 1.00
s5	The induced corrections turn out to contribute at leading order to the central charges and levels, which in turn determine the black hole entropy.	result 0.79	0.92	0.55	asserted 1.00

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Original 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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References

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Revisiting the Quantum Geometry of Torus-fibered Calabi-Yau Threefolds
hep-th 2025-10 conditional novelty 7.0 of 10

The conjectured Jacobi modularity of topological string amplitudes on torus-fibered Calabi-Yau threefolds is derived conditionally from the wave-function property under the relative conifold monodromy, which also maps...
The Swampland Distance Conjecture for Kahler moduli
hep-th 2018-12 conditional novelty 6.0 of 10

In the Kähler moduli space of Calabi-Yau threefolds, every infinite-distance limit carries an explicit infinite family of wrapped-brane charges, generated by monodromy, that becomes massless relative to the Planck scale.

How the literature uses it

11 arXiv papers cite this in 43 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 30 sentences without a confident label

Contests it 1 paper

However, it was shown in [ref] that this is not the full story and does not generically reproduce the correct microscopic results.

Black Holes and (0,4) SCFTs from Type IIB on K3 · Macroscopics of 6d strings · contest 0.75

Builds on it 1 paper

The macroscopic computations for Taub-NUT performed in [ref] straightforwardly extend to the ALE and ALF transverse spaces considered here.

Black Holes and (0,4) SCFTs from Type IIB on K3 · Conclusion and outlook · 0.99

Uses its method or tool 2 papers

Instead the correct procedure is to reduce the action on the compact part of the asymptotic geometry [ref] .

Anomalies of (0,4) SCFTs from F-theory · Classical contributions · 0.81
Following [ref] we use zeta-function regularization.

Black Holes and (0,4) SCFTs from Type IIB on K3 · Contribution of massive KK modes to one-loop Chern–Simons terms · 1.00

Compares with it 2 papers

We expect that the left level can be computed by adapting the techniques in [ref] .

Black Holes and (0,4) SCFTs from Type IIB on K3 · Transverse ALF spaces: AD-series · 0.95
We can see that if we specify the ALF result to Taub-NUT we recover the classical results of [ref] as expected.

Anomalies of (0,4) SCFTs from F-theory · Total classical contributions · 0.97

Cites it as support 1 paper

In [ref] for similar settings, this assumption was shown to lead to results which agree with the microscopic predictions.

Anomalies of (0,4) SCFTs from F-theory · Quantum contributions to levels · 0.96

Cites it as background 2 papers

More recently black holes in F-theory [ref] have been given further consideration in [ref] for example.

Black Holes and (0,4) SCFTs from Type IIB on K3 · Introduction · 0.96
In a tangential direction, there have been further advancements in studying black strings in F-theory probing various four-dimensional asymptotically flat spaces [ref] using their AdS$_3$ near-horizon geometries.

On Type IIA AdS$_3$ solutions and massive GK geometries · Introduction · 0.98

What it cites · 20 sentences without a confident label

Builds on 3 papers

In [ref] the authors extended the study of [ref] to the case of five-dimensional spinning black holes that previously only had been studied in compactifications of type II strings on T$^5$ and K$3 ×S^1$ [ref] .

F-Theory, Spinning Black Holes and Multi-string Branches · Introduction · 0.97
In [ref] the authors extended the study of [ref] to the case of five-dimensional spinning black holes that previously only had been studied in compactifications of type II strings on T$^5$ and K$3 ×S^1$ [ref] .

D--branes and Spinning Black Holes · Introduction · 0.97
In [ref] the authors extended the study of [ref] to the case of five-dimensional spinning black holes that previously only had been studied in compactifications of type II strings on T$^5$ and K$3 ×S^1$ [ref] .

Black Holes and Calabi-Yau Threefolds · Introduction · 0.97

Uses the method or tool of 1 paper

The microscopic analysis was carried out by mapping the F-theory setup to the MSW setting [ref] .

Black Hole Entropy in M-Theory · Introduction · 0.84

Compares with 4 papers

From a six-dimensional supergravity perspective we reproduced the central charges and levels of the CFT corresponding to the long wavelength limit of this set-up, which were calculated from a microscopic viewpoint via M-theory in [ref] .

Black String Entropy and Fourier-Mukai Transform · Discussion · 0.88
[equation] Comparing conventions in [ref] and [ref] we find that we need $A^0→qiA^0$ in the counterterm above.

One-loop Chern-Simons terms in five dimensions · 6D to 5D one-loop corrections · 0.96
On the CFT side the main difference between [ref] and [ref] is the identification of an $𝔰𝔲(2)_L$ current algebra in spite of the absence of supersymmetry in the left-moving sector.

F-Theory, Spinning Black Holes and Multi-string Branches · Introduction · 0.99

Cites as background 13 papers

In particular, we use the regularized sums [equation] It is worth noting that regularizing the contributions arising from integrating out infinitely many massive modes is in general very subtle.[See [ref] for a recent detailed discussion.] Firstly, applying zeta-function regularization is only possible if the higher-dimensional theory is anomaly free [ref] .

Infinite Distances in Field Space and Massless Towers of States · One-loop Chern-Simons terms from KK spectrum · 0.83
In particular, we use the regularized sums [equation] It is worth noting that regularizing the contributions arising from integrating out infinitely many massive modes is in general very subtle.[See [ref] for a recent detailed discussion.] Firstly, applying zeta-function regularization is only possible if the higher-dimensional theory is anomaly free [ref] .

Chiral anomalies on a circle and their cancellation in F-theory · One-loop Chern-Simons terms from KK spectrum · 0.83
This is the four-dimensional side of the correspondence in [ref] .

Exploring the relation between 4D and 5D BPS solutions · Introduction · 0.90

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