Partition Functions for Supersymmetric Black Holes

Manschot, Jan

doi:10.5117/9789056295400

Cited by 6 publications

(9 citation statements)

References 141 publications

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“…Entropy from conformal field theory. As an elementary check of our results, we reproduce the results in [18,19,61,62] by specialising them to the large charge limit so as to approach the Wald entropy of the black hole. This allows matching the entropy, computed from the elliptic genus, to the leading-order behaviour of |Z| 2 .…”

Section: Jhep11(2021)032mentioning

confidence: 94%

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Attractors with large complex structure for one-parameter families of Calabi-Yau manifolds

Candelas

Kuusela

McGovern

2021

J. High Energ. Phys.

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The attractor equations for an arbitrary one-parameter family of Calabi-Yau manifolds are studied in the large complex structure region. These equations are solved iteratively, generating what we term an N-expansion, which is a power series in the Gromov-Witten invariants of the manifold. The coefficients of this series are associated with integer partitions. In important cases we are able to find closed-form expressions for the general term of this expansion. To our knowledge, these are the first generic solutions to attractor equations that incorporate instanton contributions. In particular, we find a simple closed-form formula for the entropy associated to rank two attractor points, including those recently discovered. The applications of our solutions are briefly discussed. Most importantly, we are able to give an expression for the Wald entropy of black holes that includes all genus 0 instanton corrections.

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Section: Jhep11(2021)032mentioning

confidence: 94%

“…As in [61], we concentrate on the special case where q = 0 for clarity. From the Cardy formula, we find the asymptotic expression…”

Section: Jhep11(2021)032mentioning

confidence: 99%

Attractors with large complex structure for one-parameter families of Calabi-Yau manifolds

Candelas

Kuusela

McGovern

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…As an elementary check of our results, we reproduce the results in [15,16,54,55] by specialising them to the large charge limit so as to approach the Wald entropy of the black hole. This allows matching the entropy, computed from the elliptic genus, to the leading-order behaviour of |Z| 2 .…”

Section: Entropy From Conformal Field Theorymentioning

confidence: 94%

“…From this we identify, using the transformations in appendix C, p = κ, q = −κ (Υ + Y 110 ) and q 0 = κ 2 (2Λ + Y 100 ). As in [54], we concentrate on the special case where q = 0 for clarity. From the Cardy formula, we find the asymptotic expression…”

Section: Entropy From Conformal Field Theorymentioning

confidence: 99%

Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds

Candelas,

Kuusela,

McGovern

2021

Preprint

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The attractor equations for an arbitrary one-parameter family of Calabi-Yau manifolds are studied in the large complex structure region. These equations are solved iteratively, generating what we term an N -expansion, which is a power series in the Gromov-Witten invariants of the manifold. The coefficients of this series are associated with integer partitions. In important cases we are able to find closed-form expressions for the general term of this expansion. To our knowledge, these are the first generic solutions to attractor equations that incorporate instanton contributions. In particular, we find a simple closed-form formula for the entropy associated to rank two attractor points, including those recently discovered. The applications of our solutions are briefly discussed. Most importantly, we are able to give an expression for the Wald entropy of black holes that includes all genus 0 instanton corrections.

show abstract

“…In deriving (2.22) we have neglected the momentum modes on R 3 . Including those modes in the right-hand side of (2.21) and extracting their contribution, one can use (2.33) to derive that [25]…”

Section: Modular Transformation Propertiesmentioning

confidence: 99%

On the exact entropy of $\mathcal{N}=2$ black holes

Gomes,

Lam,

Mathys

2019

Preprint

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We study the exact entropy of four-dimensional N = 2 black holes in M-theory both from the brane and supergravity points of view. On the microscopic side the degeneracy is given by a Fourier coefficient of the elliptic genus of the dual two-dimensional N = (0, 4) SCFT and can be extracted via a Rademacher expansion. We show how this expansion is mapped to a modified OSV formula derived by Denef and Moore. On the macroscopic side the degeneracy is computed by applying localization techniques to Sen's quantum entropy functional reducing it to a finite number of integrals. The measure for this finite dimensional integral is determined using a connection with Chern-Simons theory on AdS 2 ×S 1 . The leading answer is a Bessel function in agreement with the microscopic answer. Other subleading corrections can be explained in terms of instanton contributions.

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Partition Functions for Supersymmetric Black Holes

Cited by 6 publications

References 141 publications

Attractors with large complex structure for one-parameter families of Calabi-Yau manifolds

Attractors with large complex structure for one-parameter families of Calabi-Yau manifolds

Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds

On the exact entropy of $\mathcal{N}=2$ black holes

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