Black Holes and Calabi-Yau Threefolds

Cumrun Vafa

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Black Holes and Calabi-Yau Threefolds

Cumrun Vafa

High Energy Physics - Theory · Submitted 10 Nov 1997

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

The authors' main claim The macroscopic entropy in the 5 dimensional case predicts a surprising growth in the cohomology of moduli space of holomorphic curves in Calabi-Yau threefolds which we verify in the case of elliptic threefolds.

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We compute the microscopic entropy of certain 4 and 5 dimensional extermal black holes which arise for compactification of M-theory and type IIA on Calabi-Yau 3-folds. The results agree with macroscopic predictions, including some subleading terms. The macroscopic entropy in the 5 dimensional case predicts a surprising growth in the cohomology of moduli space of holomorphic curves in Calabi-Yau threefolds which we verify in the case of elliptic threefolds.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the microscopic entropy of certain 4 and 5 dimensional extermal black holes which arise for compactification of M-theory and type IIA on Calabi-Yau 3-folds.	contribution 1.00	0.95	0.12	asserted 1.00
s1	The results agree with macroscopic predictions, including some subleading terms.	result 0.99	0.82	0.33	asserted 1.00
s2	The macroscopic entropy in the 5 dimensional case predicts a surprising growth in the cohomology of moduli space of holomorphic curves in Calabi-Yau threefolds which we verify in the case of elliptic threefolds.	result 0.85	0.90	0.46	asserted 0.99

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Original abstract

We compute the microscopic entropy of certain 4 and 5 dimensional extermal black holes which arise for compactification of M-theory and type IIA on Calabi-Yau 3-folds. The results agree with macroscopic predictions, including some subleading terms. The macroscopic entropy in the 5 dimensional case predicts a surprising growth in the cohomology of moduli space of holomorphic curves in Calabi-Yau threefolds which we verify in the case of elliptic threefolds.

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References

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Cited by 19 Pith papers

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How the literature uses it

36 arXiv papers cite this in 57 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 · 34 sentences without a confident label

Builds on it 2 papers

Before we proceed to a complicated example such as quintic, in the next section we review (and extend) the results in [ref] for compactification of M-theory on an elliptic Calabi-Yau threefold.

Black Hole Entropy for M-theory on the Quintic Threefold via F-theoretic Strings · 5 dimensional BPS black holes · 0.89
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] .

Four-dimensional black hole entropy from F-theory · Introduction · 0.97

Compares with it 6 papers

Moreover, as discussed in Section [ref], by lifting the solution to five dimensions and enforcing a parametrically small horizon radius compared to the size of the internal circle (whenever possible), one finds perfect agreement with the microscopic counting [ref] and one-loop exact computations in the dual M-theory description [ref] .

Black Hole Entropy, Quantum Corrections and EFT Transitions · Conclusions and Outlook · 0.81
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.

Four-dimensional black hole entropy from F-theory · Introduction · 0.99
Our results for the entropy agree with the results of microscopic counting for large black holes [ref] and for black rings [ref] .

Near-horizon analysis of D=5 BPS black holes and rings · Introduction · 0.96

Cites it as background 13 papers

Along with the original reference [ref] which studied five-dimensional non-spinning black holes in compactifications of type II strings on T$^5$ and K$3 ×S^1$, the most prominent examples are five-dimensional non-spinning black holes in compactifications of M-theory on a Calabi-Yau threefold CY$_3$ [ref] , and four-dimensional black holes in M-theory on CY$_3 ×$ S$^1$ [ref] .

Four-dimensional black hole entropy from F-theory · Introduction · 0.91
Extremal black holes, which have the minimum amount of mass given their charge, have been studied extensively in the context of string theory (see e.g., [ref] ).

Non-Holomorphic Cycles and Non-BPS Black Branes · Black holes and strings in M-theory on a Calabi-Yau threefold · 1.00
There have been several detailed accounts of the M5-brane wrapped on cycles of a generic Calabi-Yau manifold, for example see [ref] , and also the M5-brane on $K3$ [ref] .

The M5-brane on K3 x T^2 · Introduction · 0.99

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