Pith. sign in

REVIEW 3 major objections 6 minor 2 cited by

The Superconformal Index and Black Hole Instabilities

T0 review · 3 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

Pith's one-line read This paper claims that the two-fugacity superconformal index of $\mathcal{N}=4$ supersymmetric Yang-Mills at finite $N$ systematically exceeds the entropy of single-center supersymmetric AdS$_5$ black holes at large $J_R$, signalling grey…

desk verdict The new two-fugacity index numerics are solid, but the grey galaxy claim is built on a comparison to equal-charge black hole entropy that the index's own charge-sector mixing undermines. read the letter →

arxiv 2502.01614 v2 pith:MWCRD7P4 submitted 2025-02-03 hep-th gr-qc

classification hep-thgr-qc
keywords superconformalindexN=4supersymmetricYang-MillsAdS5blackholeentropygreygalaxiesgiantgravitonexpansionfiniteNtwoangularmomentamicrocanonicaldegeneracy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper numerically evaluates the superconformal index of $\mathcal{N}=4$ supersymmetric Yang-Mills at finite gauge-group rank $N$, tracking both the combination $j=6(J_L+Q)$ and the angular-momentum difference $J_R$. It compares the resulting degeneracies with the entropy of supersymmetric AdS$_5$ black holes with two distinct angular momenta and finds a systematic excess at large $J_R$, where the black hole entropy is expected to vanish. The authors interpret this excess as evidence that the index counts not only the single-center black hole but also 'grey galaxy' configurations, in which the black hole is surrounded by a gas of gravitons. The paper also shows that the giant graviton expansion with up to two giants is a numerically efficient way to reach rank $N=15$ and charge $j=107$, far beyond what direct character evaluation allows. If the interpretation is right, the index is a sharper probe of the space of supersymmetric gravity solutions than previously thought.

What carries the argument

The central object is the two-fugacity superconformal index $I_N(x,p)$ obtained by the fugacity rescaling $p\to p x^3$, $q\to x^3/p$, $y_a\to x^2$, so the index counts states by $j=6(J_L+Q)$ and $J_R$. This is the equal-fugacity limit of the refined index, where all three R-charge chemical potentials are set equal but states with unequal charges are still counted. The argument is carried by two computational mechanisms: direct plethystic exponentiation over $U(N)$ characters with a polynomial-fit trick that reduces the two-variable expansion to many single-variable expansions, efficient for $N\le 4$; and the giant graviton expansion $I_N/I_\infty = 1 + \sum_m G_N^{(m)}$, where the $m$-th giant enters at $j=2m(N+m)$, which lets the authors reach $N=15$ with two giants. The expansion is truncated at $m=2$, and comparisons are made in the $j$-range where the truncation is reliable, up to $j=107$ for $N=15$. The black hole entropy side uses the entropy $S=2\pi\sqrt{3Q^2 - N^2 J_L}$ together with the charge constraint solved for $J_L(j,J_R)$.

What would settle it

Compute the index with the equal-charge constraint imposed microcanonically—that is, expand the fully refined index in $x$, $p$, $y_1$, $y_2$, discard all terms with unequal R-charges, and compare the resulting degeneracies with $S(j,J_R)$. If the large-$J_R$ tails disappear entirely, the claimed grey-galaxy contribution is an artifact of counting unequal-charge states. A complementary check would be to compute the on-shell entropy of the grey galaxy configuration at the same $(j,J_R)$ and see whether its logarithm matches the index degeneracy in the tail region.

Watch

Extended reading notes

Core claim

The central discovery is that when the superconformal index is refined by two fugacities (one tracking $j=6(J_L+Q)$ and one tracking $J_R$), its finite-$N$ degeneracies $d_N(j,J_R)$ systematically exceed the entropy of the corresponding single-center supersymmetric AdS$_5$ black hole in the region of large $|J_R|$. For $U(4)$ at $j=98$, for instance, the index degeneracy remains nonzero up to $J_R=15$ while the black hole entropy reaches zero at $J_R \sim 11.5$, with the divergence starting at $J_R=11$. The same qualitative behavior appears for $U(2)$, $U(3)$, $U(10)$ and $U(15)$, across $j \sim 100$ and $j \sim 200$, so the deviation is not an artifact of a single $N$ or charge. The authors take this as evidence that the index contains microphysical information about additional phases, specifically grey galaxies, whose contribution grows as $J_R$ approaches its maximal value. They further establish the giant graviton expansion, truncated at two giants, as a practical numerical tool that gives access to $N=15$ at $j$ up to $107$.

Load-bearing premise

The comparison assumes that the equal-fugacity index, which counts states with arbitrary distributions of R-charge, can stand in for the microcanonical entropy of black holes with three equal charges; if mixed-charge states dominate the large-$J_R$ tails, the observed deviation is a charge-sector artifact rather than a grey-galaxy phase.

Editorial extensions

If this is right

  • If the interpretation is correct, the superconformal index is not blind to the phase structure of supersymmetric solutions: its degeneracies carry contributions from grey galaxy configurations whenever the conserved charges allow them.
  • The finite-$N$ index will continue to deviate from the single-center black hole entropy at large $|J_R|$ as $N$ grows; the $U(10)$ and $U(15)$ results indicate the tail persists and may lengthen at higher $N$.
  • A quantitative match between the index tail and the on-shell entropy of explicit grey galaxy solutions would turn the observed deviation into a microscopic count of those configurations.
  • The giant graviton expansion truncated at a few giants is a viable numerical route to finite-$N$ indices in regimes where character methods become intractable; higher $j$ will require including the third giant at $j=6(N+3)$.

Reading between the lines

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

  • A natural next check is to compute the index with the microcanonical equal-charge constraint, discarding states with unequal R-charges, and see whether the large-$J_R$ tails survive; the present paper leaves that computation open.
  • The same two-fugacity comparison should be portable to AdS$_4$/SCFT$_3$ indices, where grey galaxy phases have also been argued, using index evaluation methods that include monopole contributions.
  • If the tails are genuine, their shape and endpoint should be reproducible from a saddle-point analysis of the index with complex chemical potentials, which would give an analytic handle on the critical $J_R$ at which the black hole gives way to the grey galaxy.
  • The growth of the tail with $N$ suggests that at large $N$ the grey galaxy contribution may become comparable to the black hole entropy over an extended window in $J_R$, shifting predictions for the phase diagram beyond the equal-charge locus.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This manuscript reports a numerical study of the two-fugacity superconformal index of N=4 SYM with gauge group U(N), defined with equal R-charge fugacities and unequal angular-momentum fugacities in Eq. (2.8). From the coefficients d_N(j,J_R) of x^j p^{2J_R}, the authors compare the logarithm of the degeneracy with the entropy S(j,J_R) of equal-charge supersymmetric AdS5 black holes given in Eqs. (4.1)-(4.5). The central observation is that the index entropy tracks the black-hole entropy for small |J_R| but shows a systematic excess at large |J_R| (Figs. 4-5), which the authors interpret as evidence that the index registers phases beyond the single-center black hole, specifically grey galaxies (§4.3, §5). The paper also develops a numerical implementation of the giant graviton expansion as a complement to direct character evaluation: the m=2 truncation is exact below j=6(N+3), permitting N=15, j=107 with modest resources, and the single-charge results of [23,24] are reproduced as calibration.

Significance. The numerical methods and their validation are the strongest part of this paper: the character-method algorithm of Appendix A, the polynomial-fit reduction of the two-variable expansion, and the giant graviton expansion with its exactness thresholds are clearly described and cross-checked against the known single-charge results, and the m=2 truncation is exact in the plotted range (j=77<78 for N=10; j=107<108 for N=15). If the grey-galaxy interpretation of the large-|J_R| tails is correct, this would be a novel use of a rigid, sign-refined Witten index to probe the space of supersymmetric gravitational phases. The central interpretive claim, however, rests on an uncontrolled comparison: the coefficient d_N(j,J_R) counts states of arbitrary R-charge assignments and angular-momentum distributions, while S(j,J_R) is the entropy of a single equal-charge black-hole sector, and the paper explicitly declines to impose the equal-charge projection (§2.3).

major comments (3)
  1. [§4.3; Eqs. (2.8), (2.11), (4.5)] The central comparison mismatches the R-charge content of the two sides, and the paper states this limitation itself: §2.2 notes that the equal-fugacity index 'still counts all states, including those with unequal charges,' and §2.3 explains that the equal-charge microcanonical projection cannot be imposed on the single-letter index and is not attempted. For fixed (j,J_R), the coefficient d_N(j,J_R) of (2.8) sums over all BPS states whose J_L and total charge satisfy j=6(J_L+Q) with Q=(Q1+Q2+Q3)/3, while the entropy (4.5) is that of the single-center black hole with Q1=Q2=Q3 and with J_L fixed by the no-CTC constraint (4.2). No argument is supplied that the equal-charge slice dominates the sum, and the relevant fluctuations are not small at the plotted parameters (for N=15, j=107 one has Q≈15, so √Q is a substantial fraction of Q). The bulk agreement documented in §4.2 at J_R=0 mildly supports equal-charge-type dominance when a black hole exists, but that control does not extend to the large-|J_R| tail where the deviation is claimed. The authors should either carry out the equal-charge projection at small N and moderate j, or provide a quantitative dominance argument, before the excess can be attributed to grey galaxies rather than to the mixing of R-charge sectors.
  2. [§4.3.1; Figs. 4–5] The tail states are kinematically consistent with graviton gas, and the paper does not separate the multi-graviton contribution I∞ from the giant-graviton corrections. Every contributing state obeys |J_R| ≤ J_L and Q = j/6 − J_L, so the plotted tail points carry very little R-charge: for U(4), j=98, J_R=13, any contributing state has (Q1+Q2+Q3)/3 ≤ 98/6 − 13 ≈ 3.3, while the entropy formula (4.1) requires 3Q² > N²J_L = 16×13, i.e., Q > 8.3, for a real black-hole entropy at N=4. Hence no single-center black hole of the family considered in §4.1 exists in this tail at all; the same conclusion holds at the extreme tails of the other panels. Such states are pure multi-graviton configurations, not 'black hole plus gas' grey galaxies, and their presence in the index is expected independently of any phase transition. To support the phase-transition claim made in §4.3.1, the authors should compare d_N(j,J_R) with the multi-graviton coefficients d_∞(j,J_R) of (3.2), or otherwise show that the excess over S(j,J_R) behaves like the entropy of a grey-galaxy (central black hole plus gas) ensemble rather than that of the gas alone.
  3. [§4.2–4.3; Figs. 4–5; Eq. (4.8)] The evidential basis for the word 'systematic' is thin and partly post hoc. The plotted quantity is the logarithm of a signed, cancellation-prone Witten-index coefficient, and the fixed-j slices are chosen to avoid the 'roughly periodic dips' where the index falls below the black-hole curve (§4.2 and §4.3). Negative coefficients occur in the two-fugacity expansion (see (4.8), where the x^6 term has coefficient −p^{−2} + 13 − p^2), so it is unclear how log d is defined where d<0; the figures should state explicitly which points are plotted and how cancellations are handled. Only two j values per gauge group are shown (j≈100 and j≈200 for N=2,3,4; single values j=77 and j=107 for N=10 and 15). For a claim of systematic deviation, a wider scan over j, including values with partial cancellations, and a quantitative characterization of the departure (for example, the critical J_R at which the index entropy first exceeds S(j,J_R), and the asymptotic slope of the tail, as functions of j and N) are needed.
minor comments (6)
  1. [§5] There are typos in the conclusions: 'surruounding' should be 'surrounded', and 'Phythia' appears to be a misspelling of 'Pythia'.
  2. [Notation] Equation (3.6) defines d(j,J_R), while §4.3 uses d_N(j,J_R); the N-dependence should be carried consistently throughout the text and figures.
  3. [Figs. 4–5 captions] The figure captions should state the numerical precision and, for the giant-graviton panels, the exactness range j < 6(N+3); the thresholds are given in the text but the panels themselves carry no indication of the truncation.
  4. [Note added] The note added acknowledges the contemporaneous work [28] with a 'comprehensive discussion of the index vis-à-vis the space of supersymmetric solutions,' but the body of the paper never engages with [28]; in revision the authors should state explicitly how their conclusions relate to [28], in particular whether that work addresses the equal-charge restriction that is central to the present comparison.
  5. [§4.2.1] The estimate m*≈((√3−1)/2)N giant gravitons needed to reach j∼N² should be reconciled with the observation that m=2 already shows agreement with the entropy curve; the observation does not invalidate the saddle estimate, but the discussion would benefit from explaining why agreement begins so early.
  6. [Appendix A] The algebraic relations quoted for N=4 (for example j1+j2+j3=0 and j1−j4−j5=0 below (A.4)) are presented without derivation; a sentence or a reference explaining their origin would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the index degeneracies and black hole entropy are independently defined quantities, compared without fitted parameters.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The superconformal index is evaluated either directly from its definition (Eq. (2.2) with the single-letter index (2.4) and Haar measure (2.3)) or from the giant graviton expansion (Eqs. (3.1)-(3.4)) taken from the independent literature [30-35], and the black hole entropy S(j, JR) is taken from the supergravity solutions of Gutowski-Reall and Kunduri-Lucietti-Reall ([41-44]) via Eqs. (4.1)-(4.5). No parameter is fitted to the index data in order to produce the entropy curve, and no quantity in the comparison is defined in terms of the other. The central claim, that the two-fugacity index systematically deviates from the equal-charge black hole entropy at large JR, is therefore not built into the input: it is an observation about two independently computed functions d_N(j, JR) and S(j, JR). The paper itself flags the most serious limitation in Sec. 2.3: the index (2.8) counts states with unequal R-charges because 'the restriction to equal charges cannot be done on the single-letter index,' and the equal-charge projection 'will not be considered further.' That is a potential validity concern about whether the comparison is apples-to-apples, but it is a matter of physical interpretation and not circularity, because the index coefficient and the black hole entropy are each obtained from independent definitions and external gravity results. The paper's self-citations ([4], [9], [25], [40], [50]) are ancillary methodological references and are not load-bearing for the central comparison. Accordingly, no circular step can be exhibited, and the appropriate score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central comparison depends on two ad hoc assumptions: that mixed-charge index degeneracies can stand in for equal-charge black hole entropy, and that log of a signed index is an entropy. The numerical methods rest on standard index and giant graviton results from the cited literature. No free parameters are fitted.

assumptions (5)
  • domain assumption The superconformal index counts BPS states and is given by Eq (2.1)-(2.4).
    Standard definition in N=4 SYM; used throughout the paper.
  • domain assumption The giant graviton expansion (3.1)-(3.3) is exact for finite N and the m-th giant contributes starting at j=2m(N+m).
    Taken from Refs. [30-35]; used for numerical evaluation in Sections 4.2.1 and 4.3.1.
  • domain assumption The black hole entropy and charge constraint are given by Eqs (4.1) and (4.2).
    Taken from Refs. [41-44]; used as the comparison baseline.
  • ad hoc to paper Index degeneracies at fixed (j,JR) from the equal-fugacity index can be compared to the equal-charge black hole entropy.
    Implicit in Section 4.3; not derived. The index counts mixed-charge states, so this is the load-bearing assumption of the comparison.
  • ad hoc to paper The logarithm of the signed index degeneracy is a proxy for an entropy.
    Implicit in Figures 4 and 5; no justification is given for why log|d| should match S_BH in the presence of sign cancellations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Superconformal Index and Black Hole Instabilities." pith.science (2026). https://pith.science/paper/MWCRD7P4

@misc{pith2026250201614,
  author       = {Pith},
  title        = {Pith review of: The Superconformal Index and Black Hole Instabilities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MWCRD7P4}},
  note         = {Machine review of arXiv:2502.01614}
}
abstract

The superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills theory with gauge group $\mathrm{U}(N)$ has provided powerful insights into the entropy of supersymmetric black holes in AdS$_5\times S^5$, including some sub-leading logarithmic and non-perturbative corrections. Recently, the phase space of supersymmetric solutions has been argued to contain configurations other than the asymptotically AdS$_5$ black hole. Such configurations include the so-called grey galaxies where the black hole at the center is surrounded by a gas of gravitons. By numerically evaluating the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills at small values of $N$, we detect systematic deviations from the entropy of black holes with two distinct angular momenta. We find that the giant graviton expansion of the index is a numerically efficient way of evaluating the index that complements the direct character evaluation and allows for explicit access to $N\le 15$ with up to two giant gravitons in the expansion. We find it remarkable that a supersymmetric quantity in field theory, usually thought of as a rigid counting observable, indeed contains information about different phases in the space of supersymmetric solutions on the gravity side.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Interior zeros of supersymmetric indices

    hep-th 2026-07 accept novelty 7.0 of 10

    Interior zeros of a supersymmetric index exist iff its arithmetic coefficients δ(ν) grow exponentially at rate set by the nearest zero, detectable from finitely many q-series terms.

  2. Equal-charge projection of the $\mathcal{N}=4$ index: exact large-$N$ formula and finite-rank $U(3)$ coefficients

    hep-th 2026-07 accept novelty 7.0 of 10

    Equal-charge projection of the N=4 index admits an exact large-N factorization into a pentagonal prefactor times the cube of the partition function, and finite-rank U(3) coefficients populate the resulting zero interv...

Reference graph

Works this paper leans on

52 extracted references · 9 canonical work pages · cited by 2 Pith papers

  1. [1]

    Cabo-Bizet, D

    A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS 5 black holes , JHEP 10 (2019) 062, [1810.11442]

  2. [2]

    S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT , 1810.12067

  3. [3]

    Benini and E

    F. Benini and E. Milan, Black Holes in 4D N =4 Super-Yang-Mills Field Theory , Phys. Rev. X 10 (2020) 021037, [ 1812.09613]. – 15 –

  4. [4]

    Gonz´ alez Lezcano, J

    A. Gonz´ alez Lezcano, J. Hong, J. T. Liu and L. A. Pando Zayas, Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions , JHEP 01 (2021) 001, [2007.12604]

  5. [5]

    Amariti, M

    A. Amariti, M. Fazzi and A. Segati, The SCI of N = 4 USp(2N c) and SO(N c) SYM as a matrix integral, JHEP 06 (2021) 132, [ 2012.15208]

  6. [6]

    Amariti, M

    A. Amariti, M. Fazzi and A. Segati, Expanding on the Cardy-like limit of the SCI of 4d N = 1 ABCD SCFTs , JHEP 07 (2021) 141, [ 2103.15853]

  7. [7]

    Cassani and Z

    D. Cassani and Z. Komargodski, EFT and the SUSY Index on the 2nd Sheet , SciPost Phys. 11 (2021) 004, [ 2104.01464]

  8. [8]

    Arabi Ardehali and S

    A. Arabi Ardehali and S. Murthy, The 4d superconformal index near roots of unity and 3d Chern-Simons theory, JHEP 10 (2021) 207, [ 2104.02051]

Show all 52 references
  1. [9]

    David, A

    M. David, A. Lezcano Gonz´ alez, J. Nian and L. A. Pando Zayas, Logarithmic corrections to the entropy of rotating black holes and black strings in AdS 5, JHEP 04 (2022) 160, [ 2106.09730]

  2. [10]

    J. a. F. Melo and J. E. Santos, Stringy corrections to the entropy of electrically charged supersymmetric black holes with AdS5 × S5 asymptotics, Phys. Rev. D 103 (2021) 066008, [2007.06582]

  3. [11]

    Bobev, V

    N. Bobev, V. Dimitrov, V. Reys and A. Vekemans, Higher derivative corrections and AdS5 black holes , Phys. Rev. D 106 (2022) L121903, [ 2207.10671]

  4. [12]

    Cassani, A

    D. Cassani, A. Ruip´ erez and E. Turetta,Corrections to AdS5 black hole thermodynamics from higher-derivative supergravity, JHEP 11 (2022) 059, [ 2208.01007]

  5. [13]

    Aharony, F

    O. Aharony, F. Benini, O. Mamroud and E. Milan, A gravity interpretation for the Bethe Ansatz expansion of the N = 4 SYM index , Phys. Rev. D 104 (2021) 086026, [ 2104.13932]

  6. [14]

    Y. Chen, M. Heydeman, Y. Wang and M. Zhang, Probing supersymmetric black holes with surface defects, JHEP 10 (2023) 136, [ 2306.05463]

  7. [15]

    Cabo-Bizet, M

    A. Cabo-Bizet, M. David and A. Gonz´ alez Lezcano, Thermodynamics of black holes with probe D-branes, JHEP 06 (2024) 193, [ 2312.12533]

  8. [16]

    S. Choi, J. Kim, S. Kim and J. Nahmgoong, Comments on deconfinement in AdS/CFT , 1811.08646

  9. [17]

    Cabo-Bizet and S

    A. Cabo-Bizet and S. Murthy, Supersymmetric phases of 4d N = 4 SYM at large N , JHEP 09 (2020) 184, [ 1909.09597]

  10. [18]

    Arabi Ardehali, J

    A. Arabi Ardehali, J. Hong and J. T. Liu, Asymptotic growth of the 4d N = 4 index and partially deconfined phases, JHEP 07 (2020) 073, [ 1912.04169]

  11. [19]

    Copetti, A

    C. Copetti, A. Grassi, Z. Komargodski and L. Tizzano, Delayed deconfinement and the Hawking-Page transition, JHEP 04 (2022) 132, [ 2008.04950]

  12. [20]

    S. Kim, S. Kundu, E. Lee, J. Lee, S. Minwalla and C. Patel, Grey Galaxies’ as an endpoint of the Kerr-AdS superradiant instability , JHEP 11 (2023) 024, [ 2305.08922]

  13. [21]

    S. Choi, D. Jain, S. Kim, V. Krishna, E. Lee, S. Minwalla et al., Dual Dressed Black Holes as the end point of the Charged Superradiant instability in N = 4 Yang Mills, 2409.18178. – 16 –

  14. [22]

    Bajaj, V

    K. Bajaj, V. Kumar, S. Minwall, J. Mukherjee and A. Rahaman, Grey Galaxies in AdS5, 2412.06904

  15. [23]

    Agarwal, S

    P. Agarwal, S. Choi, J. Kim, S. Kim and J. Nahmgoong, AdS black holes and finite N indices , Phys. Rev. D 103 (2021) 126006, [ 2005.11240]

  16. [24]

    Murthy, Growth of the 1 16 -BPS index in 4d N = 4 supersymmetric Yang-Mills theory, Phys

    S. Murthy, Growth of the 1 16 -BPS index in 4d N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 105 (2022) L021903, [ 2005.10843]

  17. [25]

    A. G. Lezcano, J. Hong, J. T. Liu and L. A. Pando Zayas, The Bethe-Ansatz approach to the N = 4 superconformal index at finite rank , JHEP 06 (2021) 126, [ 2101.12233]

  18. [26]

    Benini and G

    F. Benini and G. Rizi, Superconformal index of low-rank gauge theories via the Bethe Ansatz , JHEP 05 (2021) 061, [ 2102.03638]

  19. [27]

    Cabo-Bizet and W

    A. Cabo-Bizet and W. Li, Generalized Bethe expansions of superconformal indices , 2411.12018

  20. [28]

    S. Choi, D. Jain, S. Kim, V. Krishna, G. Kwon, E. Lee et al., Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index , 2501.17217

  21. [29]

    Kinney, J

    J. Kinney, J. M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209–254, [ hep-th/0510251]

  22. [30]

    Gaiotto and J

    D. Gaiotto and J. H. Lee, The giant graviton expansion , JHEP 08 (2024) 025, [ 2109.02545]

  23. [31]

    Imamura, Finite-N superconformal index via the AdS/CFT correspondence , PTEP 2021 (2021) 123B05, [ 2108.12090]

    Y. Imamura, Finite-N superconformal index via the AdS/CFT correspondence , PTEP 2021 (2021) 123B05, [ 2108.12090]

  24. [32]

    Bourdier, N

    J. Bourdier, N. Drukker and J. Felix, The exact Schur index of N = 4 SYM, JHEP 11 (2015) 210, [1507.08659]

  25. [33]

    Bourdier, N

    J. Bourdier, N. Drukker and J. Felix, The N = 2 Schur index from free fermions , JHEP 01 (2016) 167, [ 1510.07041]

  26. [34]

    Murthy, Unitary matrix models, free fermions, and the giant graviton expansion , Pure Appl

    S. Murthy, Unitary matrix models, free fermions, and the giant graviton expansion , Pure Appl. Math. Quart. 19 (2023) 299–340, [ 2202.06897]

  27. [35]

    J. T. Liu and N. J. Rajappa, Finite N indices and the giant graviton expansion , JHEP 04 (2023) 078, [ 2212.05408]

  28. [36]

    Ezroura, J

    N. Ezroura, J. T. Liu and N. J. Rajappa, Analytic continuation and the giant graviton expansion, JHEP 01 (2025) 028, [ 2408.02759]

  29. [37]

    J. H. Lee, Trace relations and open string vacua , JHEP 02 (2024) 224, [ 2312.00242]

  30. [38]

    Eleftheriou, S

    G. Eleftheriou, S. Murthy and M. Rossell´ o, The giant graviton expansion in AdS5 × S5, SciPost Phys. 17 (2024) 098, [ 2312.14921]

  31. [39]

    Chang and Y.-H

    C.-M. Chang and Y.-H. Lin, Holographic covering and the fortuity of black holes , 2402.10129

  32. [40]

    Deddo, J

    E. Deddo, J. T. Liu, L. A. Pando Zayas and R. J. Saskowski, Giant Graviton Expansion from Bubbling Geometry: Discreteness from Quantized Geometry , Phys. Rev. Lett. 132 (2024) 261501, [2402.19452]

  33. [41]

    J. B. Gutowski and H. S. Reall, Supersymmetric AdS(5) black holes , JHEP 02 (2004) 006, [hep-th/0401042]

  34. [42]

    J. B. Gutowski and H. S. Reall, General supersymmetric ads5 black holes , Journal of High Energy Physics 2004 (Apr., 2004) 048–048. – 17 –

  35. [43]

    H. K. Kunduri, J. Lucietti and H. S. Reall, Supersymmetric multi-charge ads5 black holes , Journal of High Energy Physics 2006 (Apr., 2006) 036–036

  36. [44]

    Z. W. Chong, M. Cvetic, H. Lu and C. N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity , Phys. Rev. Lett. 95 (2005) 161301, [hep-th/0506029]

  37. [45]

    Larsen and S

    F. Larsen and S. Lee, Microscopic entropy of AdS 3 black holes revisited , JHEP 07 (2021) 038, [2101.08497]

  38. [46]

    Larsen and S

    F. Larsen and S. Lee, Supersymmetric charge constraints on AdS black holes from free fields , JHEP 09 (2024) 118, [ 2405.17648]

  39. [47]

    S. Choi, S. Kim, E. Lee and J. Lee, From giant gravitons to black holes , JHEP 11 (2023) 086, [2207.05172]

  40. [48]

    Beccaria and A

    M. Beccaria and A. Cabo-Bizet, Large black hole entropy from the giant brane expansion , JHEP 04 (2024) 146, [ 2308.05191]

  41. [49]

    S. Choi, C. Hwang and S. Kim, Quantum vortices, M2-branes and black holes , JHEP 09 (2024) 096, [1908.02470]

  42. [50]

    Nian and L

    J. Nian and L. A. Pando Zayas, Microscopic entropy of rotating electrically charged AdS 4 black holes from field theory localization , JHEP 03 (2020) 081, [ 1909.07943]

  43. [51]

    Amariti, J

    A. Amariti, J. Nian, L. A. Pando Zayas and A. Segati, Universal Cardy-Like Behavior of 3D A-Twisted Partition Functions, 2306.05462

  44. [52]

    S. Choi, S. Jeong and S. Kim, The Yang-Mills duals of small AdS black holes , JHEP 07 (2024) 067, [2103.01401]. – 18 –

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.