Black Hole Entropy in M-Theory

Andrew Strominger; Edward Witten; Juan Maldacena

REVIEW

Black Hole Entropy in M-Theory

Juan Maldacena, Andrew Strominger, Edward Witten

High Energy Physics - Theory · Submitted 7 Nov 1997 · 28 references

Pith's verdict: The general-charge M-theory entropy count and the one-loop match are real; the one-loop macroscopic side is a special-case evaluation plus a universality argument, and the authors say so.

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arXiv IDhep-th/9711053 (version 1)

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CitationAndrew Strominger, Edward Witten, Juan Maldacena. "Black Hole Entropy in M-Theory." arXiv:hep-th/9711053 (1997). https://pith.science/paper/HVBCB5RY

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Editor's note

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This is the paper that takes the Strominger-Vafa counting off the special-case shelf and does it for a fivebrane wrapping a general ample divisor P in a Calabi-Yau, with all charges (p^A, q_0, q_A) in play. The two things worth your time: the left-moving central charge c_L = 6D + c_2·P derived from Riemann-Roch plus the self-dual two-form reduction (eqs. 3.3, 3.10-3.14), and the one-loop comparison, where the R^4 descendant in eleven dimensions gives Delta S = (c_2·P pi/6) sqrt(q-hat_0/D) and the Cardy formula reproduces it exactly. The membrane-charge section is also nice: the shift q_0 -> q-hat_0 - (1/12) D^{AB} q_A q_B falls out of the winding-mode zero-point energy, and the coefficient and sign both work. That is a genuine, independent check, not a tautology — the two sides share no machinery beyond the identification of D and P. The reader's take is right on all of this, and the circularity score of 2 is fair. I'd only push back slightly on the framing of the one-loop soft spot. The stress-test note is correct that (2.11) is evaluated with moduli frozen at their fixed-point values and that the neglect of gauge-field one-loop terms is argued rather than shown, but the authors flag both in section 2.2 in as many words. What they flag less prominently, and what I'd actually worry about, is section 4: the left-moving chiral boson ground-state energy could shift q_0 by (6D + c_2·P)/24 rather than c_2·P/24, and they note that anomaly inflow analyses were finding an extra shift proportional to D. If that D-shift is real it competes with the one-loop term they just matched. They leave it open, honestly, but it's the loose thread I'd pull. The BPS argument in 3.2 (eqs. 3.29-3.31) is heuristic — nonlinear supersymmetry mixing to argue right-moving momentum must be a multiple of [P] — and it is load-bearing for the q_A dependence, though the macroscopic side already tells you the answer. Minor: the appendix normalization is compressed but checkable. Who should read it: anyone working on precision entropy counting, and anyone thinking about higher-derivative corrections to attractor solutions. Yes, send it out; this deserves referees, and I'd cite it.

Referee report

Significance

This is a substantial and well-executed contribution. The two computations are genuinely independent — the microscopic side uses the geometry of the divisor P and the Cardy formula, the macroscopic side uses the attractor mechanism and the R⁴ term — so the agreement at two orders is a nontrivial check rather than a tautology. The identification c_L = 6D + c₂·P is a parameter-free result, and the one-loop coefficient c₂·P π/6 is a falsifiable prediction that the microscopic computation reproduces exactly. Extending the match to all charges, including membrane charge, is a meaningful advance over the special cases of [6] and the heuristic treatment of [7,8]. The paper is also notable for carrying out the comparison entirely within M-theory, without invoking string theory.

Major objections (2)

[§2.2, Eqs. (2.11)–(2.15)] The one-loop macroscopic entropy is obtained under two assumptions that the authors explicitly acknowledge: that the topological R² term (2.11) dominates over other one-loop terms involving gauge fields, and that the moduli may be frozen at their fixed-point values when evaluating it. The text states that other terms 'in principle might further correct the entropy' and that 'we do not understand the macroscopic mechanism for moduli-independence of the one loop corrections for the general case.' Since the abstract claims 'precise agreement' at one loop, the comparison is more accurately a consistency check under stated assumptions than a derivation of the one-loop entropy. This does not undermine the tree-level result or the independent microscopic computation, and the numerical match is genuine evidence for the dominance of (2.11); but the abstract and §2.2 should state the assumptions explicitly and describe the agreement as evidence for, rather than proof of, that dominance.
[§3.2, Eqs. (3.29)–(3.31)] The BPS condition that the right-moving momentum be a multiple of [P] is justified by an argument that mixes linear and nonlinear supersymmetry transformations of the goldstinos. The argument is plausible and is offered as the promised justification of the statement made earlier in §3.2, but it is heuristic rather than a derivation. It is load-bearing for the q_A dependence of the entropy, since without it the shift (3.27) would not define a supersymmetric state for generic membrane charge. The independent macroscopic match to (2.9) with the same shift provides supporting evidence, but the authors should either state the argument explicitly as a plausibility argument or supply a more direct justification.

Minor objections (6)

[Introduction, paragraph 3] The roadmap misnumbers the sections: it says 'In section 3.1 we review the macroscopic entropy formula' and 'In section 3.2 we compute the leading one loop correction,' but the macroscopic material is in §§2.1–2.2 and the sigma-model discussion is in §3. The sentence 'In section 3 we describe the (0,4) sigma model' should also be checked against the actual numbering.
[§3.2 and §4] There are several typographical errors: 'caries' should be 'carries' in §3.2, 'supressed' should be 'suppressed' in §4, and 'the the rank two antisymmetric tensor' in §3.1 has a duplicated article.
[References] Several references need correction: [14] 'Ceccoti' should be 'Cecotti'; [19] 'Berkovitz' should be 'Berkowitz'; [22] should read 'Candelas, de la Ossa, Green and Parke' with correct spacing and initials; [4] is missing a comma between 'Gubser' and 'I. Klebanov'; and [18] gives a truncated arXiv number, 'hep-th/970617', which should presumably be 'hep-th/9706175'.
[§3, Eqs. (3.4) and (3.27)] The notation q⁰, q̂₀ and q̃₀ is used in close proximity, with q̃₀ appearing in the Cardy formula (3.4) and q̂₀ in the macroscopic formula (2.8), and their relation given only in (3.27). A short sentence at the point of first use reconciling the three symbols would help the reader.
[§3, paragraph after Eq. (3.4)] The interpolation between the microscopic regime D ≪ V_M and the supergravity regime D ≫ V_M (Eq. 2.10) assumes that no BPS states jump across the hypermultiplet moduli space. The authors state this assumption, which is standard, but it is worth flagging explicitly as an assumption underlying the comparison rather than a derived result.
[§4] The α′ discussion leaves the shift of q⁰ ambiguous between (6D + c₂·P)/24 and c₂·P/24, and cites anomaly-inflow analyses [26,27] that find an extra shift proportional to D. This is appropriately flagged as open, but a sentence on whether the ambiguity could affect the one-loop comparison of §3.1 would clarify the scope of the result.

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The paper

The paper claims

A wrapped fivebrane's left-moving modes account for an extremal black hole's entropy, including its first quantum correction.

The reading

This paper asks whether the entropy of an extremal black hole in M-theory on a Calabi-Yau threefold times a circle can be counted microscopically all the way through the first quantum correction, not just at leading order. The proposed answer is yes: the black hole is a fivebrane wrapped on a four-cycle $P$ inside the Calabi-Yau and on the circle, and the charge-carrying states are the left-moving excitations of a two-dimensional $(0,4)$ $\sigma$ model on that circle. Counting those excitations gives $S=2pi sqrt{c_L hat q_0/6}$ with $c_L = 6D + c_2cdot P$, and expanding in inverse powers of the charge reproduces the classical area law $2pi sqrt{Dhat q_0}$ at leading order and a definite one-loop term at the next order. The reason a sympathetic reader should care is that the one-loop piece is computed independently on the gravity side from a topological curvature-squared term descending from the eleven-dimensional $R^4$ interaction, and the two numbers agree with no adjustable parameter. The paper also shows how membrane charge enters: it shifts the momentum available to the oscillators, $q_0 = hat q_0 - frac{1}{12}D^{AB}q_A q_B$, which is exactly the shift the macroscopic formula requires.

What carries the argument

Three pieces of machinery carry the argument. First, the moduli of the four-cycle are counted by a Riemann-Roch index: for very ample $P$ the higher cohomology vanishes, so $dim H^0(M,L) = int_M (P^3/6 + P c_2(M)/12)$ and the number of real moduli of $P$ is $d_P = int_M (P^3/3 + P c_2(M)/6) - 2$. Second, the reduction of the fivebrane's self-dual three-form field strength on $P$ gives $b^+_2$ right-moving and $b^-_2$ left-moving scalars, with $b^pm_2$ obtained from the Euler characteristic and signature of $P$ via $c_1(P) = -[P]$ and $c_2(P) = c_2(M) + [P]^2$; the Lefschetz hyperplane theorem kills $b_1(P)$ and hence the left-moving fermions. Together these give $c_L = 6D + c_2cdot P$ and $c_R = 6D + frac{1}{2}c_2cdot P$, so the Cardy-like formula $S = 2pi sqrt{c_L tilde q_0/6}$ produces both the area law and the one-loop term. Third, the BPS condition on membrane charge: a nonzero right-moving momentum is allowed provided it is a multiple of $[P]$, because the distinguished right-moving mode from $b sim [P]$ sits with the translational zero modes and goldstinos in a $(0,4)$ multiplet, so the broken linear supersymmetries are replaced by combinations of linear and nonlinear ones, $epsilon_{nlin} = -k_R gamma_4 epsilon_{lin}$.

Extended reading notes

Core claim

The central claim is that the microscopic entropy of an extremal $N=2$, $d=4$ black hole arising from M-theory on $M times S^1$ agrees with the macroscopic Bekenstein-Hawking formula at tree level and at one loop. The microscopic object is a fivebrane wrapping $P times S^1$, with $P$ a very ample divisor of the Calabi-Yau threefold $M$; its low-energy dynamics on the circle is a $(0,4)$ $\sigma$ model whose target includes the moduli of $P$ and the scalars coming from the self-dual two-form on the fivebrane worldvolume. Counting left-moving states gives $S_{micro} = 2pi sqrt{(6D + c_2cdot P)q_0/6}$, which expanded in $1/D$ reads $2pi sqrt{D q_0} + frac{c_2cdot P, pi}{6}sqrt{q_0/D} + dots$. The first term is the classical area law $2pi sqrt{Dhat q_0}$; the second is precisely the correction $Delta S = frac{c_2cdot P, pi}{6}sqrt{hat q_0/D}$ that the authors derive on the gravity side from the four-dimensional term $frac{1}{96pi}int c_{2A}mathrm{Im}Z_A, R wedge *R$, itself a descendant of the $R^4$ term of eleven-dimensional M-theory. Membrane charge $q_A$ is carried by winding modes of the two-form scalars, and its effect on the entropy is entirely through the shift of $q_0$ by $-frac{1}{12}D^{AB}q_A q_B$, matching the macroscopic formula including sign and coefficient.

Load-bearing premise

The one-loop agreement rests on the assumption that the entropy correction is dominated by the topological curvature-squared term descending from the eleven-dimensional $R^4$ interaction, while other one-loop terms involving gauge fields that are nonzero in the black hole background are taken not to contribute; the authors acknowledge in section 2.2 that these terms 'in principle might further correct the entropy' and that the topological nature of the term 'suggests' rather than proves its dominance.

Editorial extensions

If this is right

The leading Bekenstein-Hawking entropy $2pi sqrt{Dhat q_0}$ of these extremal M-theory black holes is reproduced by state counting, including the correct dependence on all electric and magnetic charges.
The one-loop correction $frac{c_2cdot P, pi}{6}sqrt{hat q_0/D}$ has a microscopic origin as a subleading contribution to the left-moving central charge of the two-dimensional sigma model, rather than as a curvature correction with independent status.
Membrane charge need not break supersymmetry: BPS states exist for any right-moving momentum that is a multiple of the divisor class $[P]$, which explains why the relevant charge lattice is the sublattice $Gamma_M = H^2(M,mathbb{Z})$ rather than all of $H^2(P,mathbb{Z})$.
Because the black hole degrees of freedom map to deformations of a fivebrane 'foam', the counting is geometric and requires no use of string theory itself: eleven-dimensional supergravity, Calabi-Yau compactification and the fivebrane as a soliton suffice.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The agreement is a check of the $(0,4)$ sigma model's central charge against a gravitational effective action, so it can be read as evidence that the fivebrane worldvolume theory is the correct microscopic description even where the eleven-dimensional geometry is strongly curved.
Since the one-loop term is topological, one could test the result on a concrete case such as the hyperplane divisor of the quintic, where $D$ and $c_2cdot P$ are explicit integers, and compare the two sides numerically rather than order by order.
The paper's own remark that anomaly inflow analyses find an extra shift proportional to $D$ suggests the $alpha'$ sector is where the current accounting is incomplete, and a refined treatment of the chiral boson ground-state energy would be the natural place to look.
The technique of extracting a central charge from divisor moduli plus a self-dual tensor generalises to other compactifications, so the same bookkeeping could be applied to black holes whose horizon geometry is not a smooth ample divisor.

Original abstract

Extremal black holes in M-theory compactification on $M\times S^1$ are microscopically represented by fivebranes wrapping $P\times S^1$, where $M$ is a Calabi-Yau threefold and $P$ is a four-cycle in $M$. Additional spacetime charges arise from momentum around the $S^1$ and expectation values for the self-dual three-form field strength in the fivebrane. The microscopic entropy of the fivebrane as a function of all the charges is determined from a two-dimensional $(0,4)$ sigma model whose target space includes the fivebrane moduli space. This entropy is compared to the macroscopic formula. Precise agreement is found for both the tree-level and one-loop expressions.

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, 4,295 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.89 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Extremal black holes in M-theory compactification on $M\times S^1$ are microscopically represented by fivebranes wrapping $P\times S^1$, where $M$ is a Calabi-Yau threefold and $P$ is a four-cycle in $M$. Additional spacetime charges arise from momentum around the $S^1$ and expectation values for the self-dual three-form field strength in the fivebrane. The microscopic entropy of the fivebrane as a function of all the charges is determined from a two-dimensional $(0,4)$ sigma model whose target space includes the fivebrane moduli space. This entropy is compared to the macroscopic formula. Precise agreement is found for both the tree-level and one-loop expressions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
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s0	Extremal black holes in M-theory compactification on $M\times S^1$ are microscopically represented by fivebranes wrapping $P\times S^1$, where $M$ is a Calabi-Yau threefold and $P$ is a four-cycle in $M$.	background 0.59	0.20	0.05	asserted 1.00
s1	Additional spacetime charges arise from momentum around the $S^1$ and expectation values for the self-dual three-form field strength in the fivebrane.	background 0.61	0.28	0.03	asserted 1.00
s2	The microscopic entropy of the fivebrane as a function of all the charges is determined from a two-dimensional $(0,4)$ sigma model whose target space includes the fivebrane moduli space.	method 0.97	0.80	0.08	asserted 1.00
s3	This entropy is compared to the macroscopic formula.	contribution 0.45	0.83	0.07	asserted 0.81
s4	Precise agreement is found for both the tree-level and one-loop expressions.	result 1.00	0.90	0.79	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

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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Multicentered BPS black hole solutions lifted to asymptotically AdS3 x S2 show that small supersymmetric BTZ black holes are unstable to localizing on the sphere, matching the four-dimensional Entropy Enigma.
Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
hep-th 2007-10 conditional novelty 7.0 of 10

Near-extremal black hole entropy equals the entanglement entropy between two dual conformal quantum mechanics on the two AdS2 boundaries, supported by a BTZ microscopic counting and an exact free-fermion computation.
Exact Counting of Black Hole Microstates
hep-th 2004-09 conditional novelty 7.0 of 10

Including all higher-curvature F-term corrections in Wald's entropy formula reproduces, to all orders in a large-charge expansion, the microscopic degeneracy of two-charge BPS black holes in N=4 string theory.
Exact solutions for supersymmetric stationary black hole composites
hep-th 2003-04 accept novelty 7.0 of 10

The full metric, scalars and gauge fields of a multi-centered BPS black hole composite are obtained in closed form from the single-black-hole entropy function.
Superpotentials and Membrane Instantons
hep-th 1999-07 conditional novelty 7.0 of 10

Wrapped M2 branes on rigid associative 3-cycles in G2 manifolds induce a nonzero superpotential proportional to the order of the first homology group of the cycle, destabilizing many M-theory vacua.
Corrections to macroscopic supersymmetric black-hole entropy
hep-th 1998-12 accept novelty 7.0 of 10

Including squared-Riemann curvature terms and using Wald's entropy formula, the macroscopic entropy of extremal N=2 black holes matches the microscopic state count for Calabi-Yau compactifications.
Non-abelian Tensor-multiplet Anomalies
hep-th 1998-08 conditional novelty 7.0 of 10

Assuming M-theory fivebrane anomalies cancel at all charges, the authors derive the exact R-symmetry anomaly polynomial of the A_N (0,2) tensor-multiplet theories and recover the Maldacena-Strominger-Witten black hole...
BMPV black holes in higher-derivative supergravity
hep-th 2026-08 conditional novelty 6.0 of 10

The four-derivative corrected BMPV black hole is constructed directly in five dimensions, with vector-type invariants shown to leave the solution and entropy unchanged.
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.
Localizing Momentum Waves on Mazes
hep-th 2026-08 conditional novelty 6.0 of 10

On a pure M5 brane background, the linear system from the 'waves on mazes' proposal captures all null momentum waves, which localize on an AdS3 slice in both singular and smooth bump forms.
Information-Theoretic Black Hole Entropy I: Beyond the Area Law
hep-th 2026-08 conditional novelty 6.0 of 10

Black hole entropy is proposed to equal the Kullback-Leibler divergence between a mass-biased N-bit ensemble and the uniform ensemble, with the area law as the leading 1/N term.
IR Black Hole Instabilities Trigger Species-Scale Particle Production
hep-th 2026-08 conditional novelty 6.0 of 10

A mechanism is proposed in which black hole instability at the tower scale converts a fraction of the mass into particles at the species scale, with Hawking evaporation subdominant.
On conformal symmetry in large-$N$ quiver mechanics
hep-th 2026-07 conditional novelty 6.0 of 10

At large rank N, the fixed-point formula for the quiver superconformal index equals the Ω_uneq contribution to the microscopic scaling BPS index of Beaujard–Mondal–Pioline, a piece previously invisible on the Coulomb branch.
Holographic Timelike Entanglement and Subregion Complexity in Localized AdS3*S3*T4 Black Holes
hep-th 2026-07 conditional novelty 6.0 of 10

Timelike entanglement and subregion complexity detect the cap–horizon transition of localized AdS3×S3×T4 black poles via fixed-boundary-interval Lorentzian branch selection, effects absent in BTZ and large-r limits.
Berry Picking: Random Wave Chaos Hierarchy for BPS Microstate Geometries
hep-th 2026-07 conditional novelty 6.0 of 10

Wave chaos in BPS microstate geometries strengthens toward black-hole-like throats while geodesic chaos weakens, and weak-coupling CFT Renyi entropies do not share that bulk hierarchy.
Index saddle for the D1-D5-P black string and its decoupling limit
hep-th 2026-06 unverdicted novelty 6.0 of 10

Constructs index saddle for D1-D5-P black string via BPS limit and uplift, with decoupling to BTZ x S^3 computing CFT index.
On BPS Branes
hep-th 2026-06 unverdicted novelty 6.0 of 10

The paper defines cones C_BPS-B and C_BPS-BB for BPS branes in supergravity and conjectures that states in C_BPS-BB are realized as BPS states with C_BPS-B as their electric-magnetic dual when moduli-independent.
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...
Classical Unattainability of Extremality in non-BPS D-brane Systems
hep-th 2026-01 conditional novelty 6.0 of 10

For a non-BPS four-charge D-brane system in N=8 string theory, the worldline potential has no classical zero-energy minimum, so extremality is unattainable; entropy is proposed as the logarithm of the number of isolat...
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.
Mock modularity of Calabi-Yau threefolds
hep-th 2024-11 conditional novelty 6.0 of 10

The paper constructs explicit indefinite theta series solving the modular anomaly for rank 0 DT invariants, fixing these generating functions up to modular forms determined by polar terms.
An extremal black hole with a unique ground state
hep-th 2024-11 unverdicted novelty 6.0 of 10

Microscopic D-brane description of non-supersymmetric extremal black holes yields a unique ground state with non-zero energy, confirming absence of degeneracy.
Holography and the KKLT Scenario
hep-th 2022-04 conditional novelty 6.0 of 10

A holographic bound on the central charge of the dual conformal field theory forces the KKLT anti-de Sitter vacuum to sit at or below the species scale, so the effective field theory used to construct it is invalid.
Black-hole microstate spectroscopy: ringdown, quasinormal modes, and echoes
gr-qc 2021-03 conditional novelty 6.0 of 10

Three-dimensional numerical evolutions of scalar fields on multicenter fuzzball geometries reproduce black-hole ringdown, then show echoes, supporting linear stability of these horizonless microstates.
The Tadpole Problem
hep-th 2020-10 conditional novelty 6.0 of 10

The D3 charge that fluxes must spend to stabilize all complex-structure moduli appears to exceed the tadpole budget by a fixed fraction, which would rule out antibrane de Sitter uplift in long warped throats.
Distinguishing fuzzballs from black holes through their multipolar structure
hep-th 2020-07 conditional novelty 6.0 of 10

A general method for extracting multipole moments of stationary spacetimes shows that four-dimensional fuzzball microstates have multipole moments typically larger than Kerr black holes of the same mass and spin.
Swampland Constraints on 5d $\mathcal{N}=1$ Supergravity
hep-th 2020-04 conditional novelty 6.0 of 10

Unitarity of the two-dimensional worldsheet theory on magnetic monopole strings yields candidate Swampland constraints on five-dimensional supergravity, expressible as inequalities on Chern-Simons levels and, geometri...
AdS$_3$ solutions in massive IIA, defect CFTs and T-duality
hep-th 2019-09 conditional novelty 6.0 of 10

A map between AdS3 and AdS7 solutions in massive IIA supergravity shows that AdS3 solutions can be interpreted as D2-D4 defects in 6d (1,0) CFTs, with explicit global completions of the non-Abelian T-dual solution.
Two dimensional ${\cal N}=(0,4)$ quivers dual to AdS$_3$ solutions in massive IIA
hep-th 2019-09 conditional novelty 6.0 of 10

A new family of N=(0,4) AdS3 x S2 solutions in massive IIA is proposed to be dual to two-dimensional quivers made of two coupled (4,4) linear quivers, with matching central charges at large N.
1/4 BPS AdS$_3$/CFT$_2$
hep-th 2019-09 conditional novelty 6.0 of 10

A new AdS3/CFT2 holographic duality is proposed between massive Type IIA backgrounds with N=(0,4) supersymmetry and two-row quiver gauge theories, supported by a leading-order match of central charges.
Supercharging Superstrata
hep-th 2018-12 accept novelty 6.0 of 10

Acting twice with the fermionic generators of the AdS3 x S3 supergroup on a two-charge seed produces a new, simpler class of smooth horizonless D1-D5-P microstate geometries whose charges match the dual CFT.
Tensionless Strings and the Weak Gravity Conjecture
hep-th 2018-08 conditional novelty 6.0 of 10

A gauge coupling taken to zero at fixed Planck mass sits at infinite distance in moduli space, where a critical heterotic string becomes tensionless and its charged excitations populate a sublattice that satisfies the...
F-theory and AdS_3/CFT_2 (2,0)
hep-th 2017-12 conditional novelty 6.0 of 10

Varying the Type IIB axio-dilaton over the internal space yields new AdS3 solutions dual to 2d (0,2) SCFTs, with holographic and field-theory central charges agreeing to subleading order in N.
F-theory and AdS_3/CFT_2
hep-th 2017-05 accept novelty 6.0 of 10

The paper constructs the first AdS3 solutions of Type IIB supergravity with a genuinely varying axio-dilaton and shows their holographic central charges match field-theory and anomaly computations.
Chiral 2d Theories from N=4 SYM with Varying Coupling
hep-th 2016-12 accept novelty 6.0 of 10

Wrapping a D3-brane on a curve where the axio-dilaton varies produces 2d chiral theories with (0,2), (0,4), (0,6) or (0,8) supersymmetry, whose spectra and anomalies are computed and cross-checked against M5- and M2-b...
F-Theory, Spinning Black Holes and Multi-string Branches
hep-th 2015-09 conditional novelty 6.0 of 10

The elliptic genus of F-theory D3-brane strings is a meromorphic Jacobi form whose finite part yields the spinning black hole entropy and whose polar part yields subdominant states with J^2 > M^3.

See all 108 Pith citations

How later papers used it

250 later papers cite it

Evidence: substantial. 248 of the citing papers share no author with it, and 25 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 482 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

5 later papers by other authors are listed below: 1 built on it, 1 used its method or tool, 2 compared their own results with it and 1 cited it as support.

Builds on it 1 of 3 papers with this label

Described its strings as a slight extension of the MSW strings studied in this paper.

Swampland Constraints on 5d $\mathcal{N}=1$ Supergravity (2020) · 0.95 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 of 9 papers with this label

Calculated the entropy using the MSW formula of this paper.

BPS Solutions of Six-Dimensional (1,0) Supergravity Coupled to Tensor Multiplets (2018) · 0.91 · paraphrased: the licence does not allow quoting

Compares with it 2 of 14 papers with this label

To conclude this section, we consider our entropy formulae from the perspective of microstate counting and verify that in leading order our expressions agree with those in [ref] and with modular form asymptotics.

Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds (2021) · Outline of the paper · 1.00
Reported that its own formula successfully reproduces the microscopic result of this paper for a black hole with only q and p^i non-vanishing charges.

A note on modular invariant species scale and potentials (2023) · 0.90 · paraphrased: the licence does not allow quoting

Cites it as support 1 of 4 papers with this label

Said that the index equaling the CFT-index at the attractor point is consistent with this paper's account of black hole entropy.

Stability and duality in N=2 supergravity (2009) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

239 arXiv papers cite this in 469 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 · 307 sentences without a confident label

Builds on it 3 papers

One of the aims of the present work is to extend these results by including the contributions of instantons that have not been included in the approximation used in [ref] .

Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds · The central charge and entropy · 1.00
These are a slight extension of MSW strings studied in [ref] .

Swampland Constraints on 5d $\mathcal{N}=1$ Supergravity · Introduction · 0.95
This theory would be a generalization of the MSW CFT describing the BPS and near-BPS limits [ref] .

Kerr-Newman Black Holes with String Corrections · Discussion · 0.87

Uses its method or tool 9 papers

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

Four-dimensional black hole entropy from F-theory · Introduction · 0.84
Next one can use the formula (see [ref] ) [equation] to obtain ([ref]).

The M5-brane on K3 x T^2 · Counting Moduli · 0.91

Uses its data or values 1 paper

The resulting central charges, including a subleading correction proportional to the second Chern class of $M$, are [ref] c_L = 6 D + c_2·P , c_R = 6 D + c_2 ·P .

Cargese lectures on string theory with eight supercharges · The MSW CFT · 0.84

Compares with it 14 papers

This result, as noted in [ref] , matches the original field theory computation in [ref] and [ref] .

F-theory and AdS_3/CFT_2 · Leading Order Central Charges · 0.95
We will now show that ([ref]) is in perfect agreement with the microscopic M5-brane computation of the black hole entropy in the two-dimensional $(4,0)$ superconformal field theory derived by [ref] ; it also agrees with the macroscopic supergravity result [ref] .

Quantum Black Holes, Elliptic Genera and Spectral Partition Functions · Microscopic black hole entropy · 0.99
This formula should be contrasted with the result [equation] first obtained in [ref] for an ample four-cycle $P$ in a generic Calabi-Yau and extended to $K3×T^3$ and $T^6$ in [ref] .

The M5-brane on K3 x T^2 · Counting Moduli · 0.98

Cites it as support 2 papers

The $2π$ pre-factor was justified in [ref] to agree with charge quantization and also in [ref] to reproduce the correct energy density for M2-branes ending on M5-branes.

M2-Branes And The (2,0) Superalgebra · Conserved Currents · 0.96
One expects that this entropy represents the logarithm of the underlying degrees of freedom in the true theory of quantum gravity; this expectation has been successfully borne out in certain stringy models of black holes [ref] .

What is the Entropy in Entropic Gravity? · Motivation · 0.99

Cites it as background 110 papers

The dual spacetime, commonly referred to by the Maldacena, Strominger, Witten (MSW) geometry, arises from M5-branes wrapping Kähler four-cycles in a Calabi-Yau three-fold $CY_3$ [ref] :

3D gauged supergravity from wrapped M5-branes with AdS/CMT applications · Introduction · 0.81
Restricting our attention to the supersymmetric case, the first-order $α'$ corrections to the heterotic version of the “Strominger–Vafa” and “Maldacena–Strominger–Witten” black holes were obtained in [ref] , more than two decades after the corresponding two-derivative solutions had been constructed [ref] and their entropy successfully reproduced microscopically [ref] .[The $α'$ corrections to the finite-temperature black holes with three and four charges were later studied in [ref] .] Subsequently, the two-charge case —namely, the so-called small black holes— was investigated in [ref] .

BMPV black hole at first order in $\alpha'$ · Introduction · 0.89
We start with a brief review of the calculation in [ref] .

The M5-brane on K3 x T^2 · Counting Moduli · 0.80

Discussion

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