Black Hole Attractors and the Topological String

Andrew Strominger; Cumrun Vafa; Hirosi Ooguri

REVIEW

Black Hole Attractors and the Topological String

Hirosi Ooguri, Andrew Strominger, Cumrun Vafa

High Energy Physics - Theory · Submitted 17 May 2004 · 44 references

Pith's verdict: The OSV conjecture, honestly framed as a conjecture: the real new content is the mixed-ensemble reinterpretation and the Wigner-function reading, not the perturbative matching, which is a genus-by-genus check of an assumption the paper does not prove.

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arXiv IDhep-th/0405146 (version 2)

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CitationAndrew Strominger, Cumrun Vafa, Hirosi Ooguri. "Black Hole Attractors and the Topological String." arXiv:hep-th/0405146 (2004). https://pith.science/paper/5ERC2GJG

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OSV. The headline is the conjecture Z_BH = |Z_top|^2, and the paper is honest that it is a conjecture: the abstract says so, and the 'evidence' is a perturbative matching in 1/Q. What is actually new here is not the matching itself — the ingredients (topological strings compute F-terms, the attractor mechanism, F-term corrections to entropy) are all in the cited literature — but the mixed-ensemble reinterpretation in §2.3 and the Wigner-function reading in §6. The observation that the supergravity path integral naturally fixes magnetic charges and sums over electric ones with potentials φ is the conceptual move that makes the relation take the form it does, and it is the part I would actually cite. The Wigner-function reading of the degeneracies is suggestive and, as far as I know, was not in the prior literature in this form. The perturbative matching in §3.1 is done properly: the normalizations are fixed by comparing the large-volume expansions (3.6) and (3.8), and the matching is genus-by-genus, not just at the leading exponential. The genus-1 term is the order-Q^0 term, and it is matched via the c_2·t term. So the stress-test's claim that the first subleading term is 'neither computed nor matched' is wrong on the text. The real soft spot is the one the reader names: the assumption that F-terms are the only corrections to the indexed entropy. The paper calls this 'plausible' and leans on cited nonrenormalization theorems; it does not prove it. §3.2 is explicitly flagged as resting on an assumption the authors 'cannot a priori justify' and drops factors of 2 and π, so it is a heuristic, not a derivation. And the identification of Z_BH with exp[F] is a saddle-point identification: the Laplace transform (2.21) and the Legendre transform (2.22) agree only at large charges, which the authors say. The conjecture's nonperturbative content is therefore untested by the perturbative evidence, but the paper says that too. So: a well-posed conjecture with a real conceptual idea behind it, honest about its gaps. Worth a serious referee, and worth citing.

Referee report

Significance

If correct, the conjecture is a substantial result: it would reduce the indexed microstate counting of four-dimensional BPS black holes to a topological string computation, and it supplies a precise, falsifiable perturbative statement together with a novel interpretation of the black hole degeneracies as a Wigner function. The paper deserves credit for stating the conjecture sharply rather than vaguely, for fixing the normalizations through an explicit comparison of the large-volume expansions, and for labeling its own gaps: §2.3 concedes that the Legendre transform is not the inverse Laplace transform except at large electric charge, §3.2 is titled with a question mark and flags an assumption the authors say they cannot justify, and §7 lists the background-dependence issues that remain open. The perturbative matching is more than a leading-exponential coincidence: the g_top-independent terms of (3.6) and (3.8) are matched in (3.9), so the one-loop normalization is part of the evidence.

Major objections (4)

[§2.3, Eqs. (2.21)-(2.22); §3.1, Eq. (3.12)] The paper is explicit that the identification Z_BH = exp[F] in (2.22) is a saddle-point statement, since the Legendre transform is not the inverse Laplace transform of (2.21) except at large electric charge. What remains unresolved is the precise scope of the advertised 'perturbative evidence' in abstract:s1. The matching in §3.1 establishes that the saddle-point free energy equals F_top + F̄_top, with the one-loop term fixed by (3.9) and the genus-zero term by (3.10); it does not establish that the full sum over electric charges reproduces |Z_top|^2. The abstract and §1 should say this in one sentence, and should state which orders are actually matched (genus zero and one explicitly, all genera via homogeneity and the one-loop normalization). As written, a reader can come away believing the Laplace sum has been checked, which is the conjecture itself rather than the evidence for it.
[§1 and §2.2] The load-bearing premise is that the F-term corrections computed by topological strings are the only corrections to the indexed BPS entropy, so that the mixed partition function exponentiates the topological string free energy. The paper calls this 'plausible' and attributes it to supersymmetric nonrenormalization theorems in [8-10]. The authors acknowledge the gap, so the request here is not for a proof of a cited result but for a sharper statement of what class of corrections is assumed absent: for example, terms with higher powers of W^2 beyond those captured by the F_h, or hypermultiplet-dependent contributions of the kind discussed in §7.4. A concrete diagnostic would strengthen the paper considerably, since if such terms contribute to the index the relation fails already at the first subleading order and the matching in §3.1 would be a coincidence of the leading terms rather than an identity.
[§3.2] The 'simplified derivation' is presented with an assumption the authors say they 'cannot a priori justify' and with factors of 2 and π dropped. Since §3.1 already supplies a controlled derivation with normalizations fixed, §3.2 adds little and risks being read as an independent derivation of the central equation. I recommend either demoting it to a remark or labeling it explicitly as heuristic, stating in the section's first sentence what it does and does not establish.
[§5] Section 5 is presented as a set of 'possible checks' of the conjecture, but the comparison with the crystal-melting form of the topological string partition function does not check Z_BH = |Z_top|^2 directly: the crystal-melting relation is Z_crystal = Z_top, not |Z_top|^2, and the paper attributes the difference to holomorphic versus antiholomorphic moduli dependence and to an S-duality between the black hole and crystal ensembles. That resolution is asserted rather than demonstrated. Since this is one of the few places the paper attempts an independent check, the reader should be told clearly what is being checked and what is being assumed; I recommend reframing §5 as a consistency discussion rather than a check.

Minor objections (7)

[Eqs. (3.9), (3.10), and the line following (3.12)] As displayed, Eq. (3.9) reads F = -2iπ F_top, which is inconsistent with (3.11): substituting gives 2π^2 Re F_top rather than F_top + F̄_top. The coefficient should be -2i/π. Similarly, (3.10) and the line after (3.12) display g_top = ±4πi CX^0 without a denominator, which is dimensionally inconsistent with (3.4) and (3.8); the correct form is g_top = ±4πi/(CX^0). Please restore the fractions, since as printed the normalization check cannot be reproduced by the reader.
[§1, final paragraph] The introduction says 'We propose a streamlined derivation of this perturbative statement in section 3.3,' but the relevant section is 3.2 and there is no §3.3. Please correct the cross-reference.
[§2.3, sentence following Eq. (2.20)] The text writes 'SBH(qL,pΛ)' where the intended symbol is SBH(q_Λ,p^Λ). Please correct the index.
[Footnote 1] The insertion is written 'F 2(−1)^F', which is ambiguous. Please write the fermion-number insertion unambiguously, for example (−1)^F F^2 or whatever the intended combination is.
[§6] The integral representation of Ω(p,q) is described as 'a bit formal' and as requiring a suitable contour. Please state explicitly what contour is intended, or state plainly that the formula is formal and that its precise definition is part of the nonperturbative completion.
[Throughout] There are numerous typographical errors that should be cleaned up before publication, among them 'magenetic' and 'part iculary' in §1, 'superst rings' and 'thoery' and 'charaged' and 'topolgoically' in §4.1, 'secton' in §4.3, and 'topopological' in §5.1. These do not affect the physics but they impede reading.
[§7.4] The discussion of hypermultiplet dependence is explicitly speculative, and the paper offers two alternative completions (with and without t_H dependence). It would help to label this paragraph as a conjecture about the nonperturbative completion rather than as a consequence of the main proposal.

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The paper

The paper claims

The mixed partition function of a four-dimensional BPS black hole equals the squared second-quantized topological string partition function at the attractor point.

The reading

Black holes in string theory carry electric and magnetic charges. Their entropy, the logarithm of the number of microstates, is computed at leading order by the area of the horizon. The paper asks what happens when higher-derivative corrections to the gravitational action are included. Those corrections are known to be captured by topological string amplitudes on the same Calabi-Yau manifold. The authors show that if one treats the black hole path integral as fixing the magnetic charges and summing over electric charges with chemical potentials, the resulting partition function takes the form of a Legendre transform of the topological string free energy. Matching normalizations in the large-volume limit then yields the conjecture Z_BH = |Z_top|^2, where Z_top is evaluated at moduli fixed by the attractor mechanism. The paper also observes that the topological string partition function behaves as a wavefunction on the moduli space, and that the black hole degeneracies are its Wigner function. The evidence is perturbative, in an expansion in inverse graviphoton charge. The authors are explicit that the derivation is mechanical and that one assumption, that F-terms are the only corrections to the indexed entropy, is not justified a priori.

Extended reading notes

Core claim

The central assertion is that the mixed black hole partition function, with magnetic charges p^Λ fixed and electric charges q_Λ summed with potentials φ^Λ, equals the squared second-quantized topological string partition function evaluated at the attractor point: Z_BH(p^Λ, φ^Λ) = |Z_top(X^Λ)|^2 with X^Λ = p^Λ + iπφ^Λ in a suitable Kähler gauge (eq. 1.2 and eq. 3.12). If correct, black hole microstate counting reduces to a topological string computation, and the black hole degeneracies are the Wigner function of the topological string wavefunction.

Load-bearing premise

The load-bearing premise is that the F-term corrections computed by topological strings are the only corrections to the indexed BPS entropy, so that the full mixed partition function exponentiates the topological string free energy. The paper calls this 'plausible' in §1 and §2.2 and attributes it to supersymmetric nonrenormalization theorems cited from [8-10], but does not prove it. If other terms contribute to the index, the relation Z_BH = |Z_top|^2 fails even perturbatively, and the matching in §3.1 would be a coincidence of the leading terms rather than an identity.

Original abstract

A simple relationship of the form Z_BH = |Z_top|^2 is conjectured, where Z_BH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Z_top is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wavefunction defined by the topological string partition function.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,073 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

A simple relationship of the form Z_BH = |Z_top|^2 is conjectured, where Z_BH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Z_top is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wavefunction defined by the topological string partition function.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A simple relationship of the form Z_BH = \|Z_top\|^2 is conjectured, where Z_BH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Z_top is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges.	background 0.62	0.14	0.71	speculative 0.99
s1	Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given.	result 0.59	0.83	0.14	asserted 0.97
s2	The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wavefunction defined by the topological string partition function.	interpretation 0.94	0.48	0.20	asserted 0.71

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.91.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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hep-th 2010-12 conditional novelty 7.0 of 10

Localization reduces the AdS2 black hole path integral to a finite-dimensional integral whose classical integrand equals the squared topological string partition function evaluated off-shell.
Entropy Function and AdS(2)/CFT(1) Correspondence
hep-th 2008-05 conditional novelty 7.0 of 10

The classical Wald entropy of an extremal black hole equals the log of the ground-state degeneracy of a dual quantum mechanics on AdS2, giving a quantum definition of extremal black hole entropy.
Topological String Theory on Compact Calabi-Yau: Modularity and Boundary Conditions
hep-th 2006-12 conditional novelty 7.0 of 10

Boundary conditions from the conifold gap, orbifold regularity, and Castelnuovo bounds fix the holomorphic ambiguity of the topological string on one-parameter compact Calabi-Yau spaces, yielding high-genus amplitudes...
Higher Derivative Corrections to Non-supersymmetric Extremal Black Holes in N=2 Supergravity
hep-th 2006-03 accept novelty 7.0 of 10

For non-supersymmetric extremal black holes in N=2 supergravity, higher-derivative corrected entropies computed in four dimensions disagree with the five-dimensional Kraus-Larsen prediction, indicating missing terms i...
Non-Supersymmetric Attractors
hep-th 2005-07 accept novelty 7.0 of 10

Extremal black holes attract scalar moduli to charge-determined horizon values whenever the charge-dependent effective potential has a positive-definite critical point, with or without supersymmetry.
New Connections Between 4D and 5D Black Holes
hep-th 2005-03 conditional novelty 7.0 of 10

The BPS partition function of a 4D Calabi-Yau black hole equals that of a 5D spinning black hole in Taub-NUT space, which in turn equals the squared N=2 topological string partition function.
On M2-, M5-, and D3-branes from 12d anomalies: an equivariant perspective on duality
hep-th 2026-08 conditional novelty 6.0 of 10

M2, M5, and D3 brane partition functions are shown to follow from one twelve-dimensional anomaly polynomial by choosing the order of equivariant integration.
Towards OSV in AdS
hep-th 2026-06 unverdicted novelty 6.0 of 10

Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
Large Order Enumerative Geometry, Black Holes and Black Rings
hep-th 2026-05 unverdicted novelty 6.0 of 10

Numerical study of high-genus GV invariants reveals 5D indices matching BMPV black-hole entropy below a critical angular momentum and black-ring dominance above, with additional phase transitions and growth laws in PT...
An Airy Tale at Large $N$
hep-th 2025-02 conditional novelty 6.0 of 10

The paper presents numerical and analytic evidence that the large-N sphere partition function of five classes of M2-brane SCFTs, with squashing and real masses, takes the form of an Airy function to all orders in 1/N.
Classical Black Hole Probes of UV Scales
hep-th 2025-02 conditional novelty 6.0 of 10

Minimal classical BPS black holes in string compactifications track the species or KK scale in infinite-distance limits, and violations may signal inconsistent EFTs.
Navigating string theory field space with geometric flows
hep-th 2024-12 conditional novelty 6.0 of 10

The authors define a flow-based distance for flux-supported internal spaces, modify the Ricci Flow Conjecture so towers of states appear only at fixed points at infinite distance, and construct flows for type II and 1...
Gluing gravitational blocks for AdS black holes
hep-th 2019-09 conditional novelty 6.0 of 10

A universal entropy functional built from glued gravitational blocks reproduces the entropy and horizon scalar values of rotating BPS black holes and strings in AdS4 and AdS5.
The Fluid Manifesto: Emergent symmetries, hydrodynamics, and black holes
hep-th 2015-10 conditional novelty 6.0 of 10

Hydrodynamics is conjectured to be a twisted supersymmetric topological sigma model whose emergent U(1) gauge current is the entropy current, with a matching brane picture for black hole interiors.
Higgs branch localization of 3d N=2 theories
hep-th 2013-12 conditional novelty 6.0 of 10

Higgs branch localization directly produces the vortex-times-anti-vortex factorization of 3d N=2 partition functions on the squashed sphere and S^1 x S^2, extending it to more general matter content.
All solutions of the localization equations for N=2 quantum black hole entropy
hep-th 2012-08 conditional novelty 6.0 of 10

The complete bosonic localization manifold for N=2 off-shell supergravity on AdS2 x S2 is n_v+1 real parameters when the auxiliary SU(2) field strength vanishes, plus an unconstrained SU(2) triplet of one-forms and a ...
Factorisation of N = 2 theories on the squashed 3-sphere
hep-th 2011-11 conditional novelty 6.0 of 10

The partition function of abelian N=2 theories on the squashed three-sphere factorises into a product of vortex and antivortex partition functions related by a modular transformation.
Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
hep-th 2011-08 accept novelty 6.0 of 10

Half-BPS black holes in N=2 supergravity carry a logarithmic entropy correction of (1/12)(23 + n_H - n_V) ln(A_H/G_N), fixed entirely by the massless spectrum and computable from the near-horizon geometry.
A-polynomial, B-model, and Quantization
hep-th 2011-07 conditional novelty 6.0 of 10

A topological-recursion construction produces the quantum operator for a classical algebraic curve, with a proposed K-theory test for when the quantization exists.
Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
hep-th 2011-06 accept novelty 6.0 of 10

One-loop gravitational corrections to N=4 and N=8 extremal black hole entropy reproduce the microscopic index results, vanishing for N=4 and giving minus 2 ln Delta for N=8.
Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
hep-th 2009-07 conditional novelty 6.0 of 10

In c=1 matrix models and topological strings on the resolved conifold, instanton effects are controlled by Borel poles and arise from eigenvalue tunneling between sheets of a multi-valued effective potential.
Refined, Motivic, and Quantum
hep-th 2009-04 conditional novelty 6.0 of 10

The refined, motivic, and quantum refinements of BPS state counts are argued to be one and the same, with the dictionary y = L^{1/2} = -q^{1/2}, checked on the resolved conifold.
Crystal Melting and Toric Calabi-Yau Manifolds
hep-th 2008-11 conditional novelty 6.0 of 10

A colored three-dimensional crystal, built from the quiver diagram and brane tiling of a toric Calabi-Yau threefold, counts BPS bound states of D0 and D2 branes on a single D6 brane, with wall crossing mediating the r...
A Modern Fareytail
hep-th 2007-12 accept novelty 6.0 of 10

A convergent coset sum (Niebur regularization) reconstructs vector-valued modular forms of non-positive weight from their polar coefficients, replacing the non-modular fareytail transform used in AdS3/CFT2 and OSV dis...
Open string amplitudes and large order behavior in topological string theory
hep-th 2006-12 conditional novelty 6.0 of 10

Matrix-model loop equations, run on a spectral curve read off from the disk amplitude, reproduce known open topological string amplitudes on toric Calabi-Yau manifolds and give the D-brane instanton action that sets t...
A Farey Tail for Attractor Black Holes
hep-th 2006-08 conditional novelty 6.0 of 10

The elliptic genus counting BPS states of 4d attractor black holes admits a Rademacher (Farey tail) expansion whose terms map to semiclassical supergravity saddles dressed by wrapped M2-branes.
Partition functions and elliptic genera from supergravity
hep-th 2006-07 accept novelty 6.0 of 10

The elliptic genus of string/M-theory on AdS3 can be computed from bulk supergravity as a sum over geometries, reproducing the CFT Farey tail expansion.
J functions, non-nef toric varieties and equivariant local mirror symmetry of curves
math.AG 2006-03 conditional novelty 6.0 of 10

The authors conjecture, with checks to order two in ℏ and degree ten in q, that O(k)⊕O(-2-k)→P^1 has the same equivariant quantum cohomology for all k, and that QH^*(F_n) has only two isomorphism types.
Entropy Maximization in the Presence of Higher-Curvature Interactions
hep-th 2006-03 conditional novelty 6.0 of 10

Higher-curvature corrections preserve and enhance entropy maxima at conifold-type singularities for real topological string coupling, but destroy them for complex coupling.
Topological strings in generalized complex space
hep-th 2006-03 conditional novelty 6.0 of 10

A BV/AKSZ construction defines a topological sigma-model on generalized Calabi-Yau targets, recovering the A- and B-models and deriving the Kontsevich star product in the open-string sector.
Real symplectic formulation of local special geometry
hep-th 2006-03 conditional novelty 6.0 of 10

For local special geometry, the real symplectic metric g_IJ is explicitly derived as -1/(2S) H_IJ + 1/(4S^2)(S_I S_J + (HΩS)_I(HΩS)_J).
Partition function of non-supersymmetric black holes in the supergravity limit
hep-th 2006-02 conditional novelty 6.0 of 10

The paper proposes Z_ns = exp(pi^2 D(p)/(2*phi0)) as the mixed partition function of non-supersymmetric attractors, engineered so its Legendre transform equals the Bekenstein-Hawking entropy.
Observations on the Darboux coordinates for rigid special geometry
hep-th 2006-02 conditional novelty 6.0 of 10

In rigid special geometry in Darboux coordinates, the matrix M(Re F, Im F) equals minus the Hessian of the Hamiltonian S(p,q), so the Kähler metric and the c-map hyperkähler metric both follow from S.
Holographic Gravitational Anomalies
hep-th 2005-08 accept novelty 6.0 of 10

A gravitational Chern-Simons term in AdS3 shifts the left and right central charges oppositely, gives empty AdS3 a nonzero angular momentum of 4 pi beta, and fixes black hole entropy corrections exactly.
Microscopic Black Hole Entropy in Theories with Higher Derivatives
hep-th 2005-06 accept novelty 6.0 of 10

Black hole entropy in higher derivative gravity follows from extremizing a central charge function over the near-horizon AdS and sphere radii, and this agrees with Wald's formula and with the heterotic string's two ce...
Black hole entropy and moduli-dependent species scale
hep-th 2022-12 conditional novelty 5.0 of 10

A lower bound on extremal black hole entropy yields a moduli-dependent species scale that matches a topological-string proposal, supporting the conjecture that black hole and topological string partition functions are equal.
Extremal and Near-Extremal Black Holes and Near-$CFT_1$
hep-th 2018-08 conditional novelty 5.0 of 10

Charged extremal black holes respond at low energies through a time-reparametrisation mode and a gauge phase mode, both suppressed by the horizon scale, with higher partial waves contributing at somewhat higher energies.
Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
hep-th 2014-01 conditional novelty 5.0 of 10

In the Nekrasov-Shatashvili limit, the refined topological string free energies on local del Pezzo geometries are computed order by order in ℏ, with quantum corrections confined to the Coulomb (normalizable) moduli.
Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
hep-th 2008-09 conditional novelty 5.0 of 10

The degeneracy of an extremal black hole's microstates equals the finite part of a string-theory path integral on its near-horizon AdS2 geometry, with a Wilson-line insertion, reducing to Wald entropy in the classical limit.
Born-Infeld Corrections to the Entropy Function of Heterotic Black Holes
hep-th 2006-04 conditional novelty 5.0 of 10

Born-Infeld terms change the near-horizon geometry and entropy of two-charge heterotic black holes, but only yield a consistent attractor when Gauss-Bonnet terms are present.
Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited
hep-th 2006-03 conditional novelty 5.0 of 10

Using exact bosonization of N fermions, the authors derive the bosonized hamiltonian for the circle and show it reduces to a massless relativistic boson with O(1/N) cubic interactions in the large-N, low-energy limit.
Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
hep-th 2006-03 conditional novelty 5.0 of 10

The degeneracies of quarter-BPS dyons in CHL orbifolds are expressed as a Borcherds product and interpreted via the 4d-5d lift as a two-loop heterotic string partition function.
Chern-Simons Theory, Holography and Topological Strings
math.AG 2025-05 conditional novelty 4.0 of 10

A review of Chern-Simons/topological string duality with a new heuristic explanation of the conifold transition in terms of a 3-form gauge field sourced by D-branes.
Species Entropy and Thermodynamics
hep-th 2023-05 conditional novelty 4.0 of 10

Particle species in quantum gravity are assigned an entropy equal to the Bekenstein-Hawking entropy of a minimal black hole and a temperature equal to the species scale, and these quantities are argued to obey laws an...

See all 66 Pith citations

How later papers used it

159 later papers cite it

Evidence: substantial. 152 of the citing papers share no author with it, and 15 of those carry a confident label from Pith's citation classifier.

Pith read 29 of the 264 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 built on it.

Builds on it 1 of 3 papers with this label

Our approach extends straightforwardly to any spacetime geometry, where for black holes we derive an M-theoretic OSV formula [ref] .

Airy functions from quantum M-theory (2026) · Introduction · 0.80

How the literature uses it

153 arXiv papers cite this in 256 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 · 168 sentences without a confident label

Contests it 2 papers

The occurence of this phenomenon would imply a breakdown of the conjecture of [ref] , which was supposed to work at weak coupling.

Subleading and non-holomorphic corrections to N=2 BPS black hole entropy · Introduction · contest 0.76
Therefore, it seems to be certain problems in the application of the OSV formula to the two charged small black holes [ref] and thus needs some further investigations.

On the Microscopic Perspective of Black Branes Thermodynamic Geometry · Fractionation of Branes: Small Black Holes · contest 0.73

Builds on it 3 papers

A relation between the indexed entropy of the BPS $N=2$ black holes and the topological string partition function, evaluated at the attractor point (horizon) has been proposed in [ref] [equation] We suggest that one may still use the relation ([ref]) for the above class of non-extremal $N=2$ black holes, with the replaced charges.

Large Charge Four-Dimensional Non-Extremal N=2 Black Holes with R^2-Terms · Introduction · 0.94
We will not dwell on these difficulties, but just formulate an analogous conjecture for orientiholes, at the same level of precision as [ref] .

Orientiholes · Relation to topological string partition function: a conjecture · 0.89
Our approach extends straightforwardly to any spacetime geometry, where for black holes we derive an M-theoretic OSV formula [ref] .

Airy functions from quantum M-theory · Introduction · 0.80

Uses its method or tool 1 paper

Treating the AdS$_3$ throat as a boundary, we can then compute the entropy of the configuration by evaluating the Cardy formula for the associated two-dimensional dual conformal field theory [ref] .

Black Hole Entropy, Quantum Corrections and EFT Transitions · Explicit gluing with the 5d solution · 0.96

Compares with it 7 papers

The leading term in the Rademacher expansion can be compared to a formula derived by Denef and Moore [ref] which is a refinement of the OSV proposal [ref] .

On the exact entropy of $\mathcal{N}=2$ black holes · Introduction · 1.00
Once again this is in exact accordance with the OSV formula, [ref] , which in this case is given by, [ref] , I^OSV_4 ∂ = i (F_4 ∂ - F̅_4 ∂ ) |_(X = φ_BPS/4 √(π); A_𝕎 = 16 π^2, A_𝕋 = 0) = φ_BPS^2 /4 π + 64 π^2 c_1 , as can be shown directly in the superconformal formalism, [ref] .

Black hole thermodynamics in natural variables: Quadrophenia · The BPS limit and the OSV formula · 0.90
is highly reminiscent of the Ooguri-Strominger-Vafa relation [ref] Z_BPS=|Z_top|^2.

Crystal Melting and Wall Crossing Phenomena · Discussion and Future Directions · 0.89

Cites it as support 2 papers

It turns out that in this case the leading count of the BPS black hole can be represented [ref] by the square of the B-model topological strings on the Calabi-Yau 3-fold:

Chern-Simons Theory, Holography and Topological Strings · Physical Implications · 0.96
Another tantalizing hint comes from Ooguri-Stromiger-Vafa (OSV) picture of black-hole partition function [ref] whereby one writes down a doubled topological string theory which localizes to the Euclidean partition function of certain asymptotically flat, supersymmetric black holes.

The Fluid Manifesto: Emergent symmetries, hydrodynamics, and black holes · Black hole story: Gravitational description · 0.98

Cites it as background 66 papers

BPS black holes in $=2$ supergravity theories have attracted revived attention recently, with the discovery of deep connections between topological strings and the entropy of four-dimensional [ref] and five-dimensional [ref] black holes, as well as a direct relation between 4D black holes and 5D black holes and black rings, often known as the 4D-5D lift [ref] .

Topological wave functions and the 4D-5D lift · Introduction · 0.99
The Ooguri-Strominger-Vafa (OSV) conjecture gives a beautiful relation between the partition function of four-dimensional BPS black holes in a type IIA string theory compactified on a Calabi-Yau and the topological A-model string partition function [ref] .

Refined Black Hole Ensembles and Topological Strings · Introduction · 0.98
One such criterion is the Swampland Distance Conjecture (SDC) [ref] , which postulates that for viable theories, infinite-distance points in the moduli space of the effective theory imply the presence of an infinite tower of massless states.

Navigating string theory field space with geometric flows · Introduction · 0.98

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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