An Index for 4 dimensional Super Conformal Theories

Juan Maldacena; Justin Kinney; Shiraz Minwalla; Suvrat Raju

REVIEW

An Index for 4 dimensional Super Conformal Theories

Justin Kinney, Juan Maldacena, Shiraz Minwalla, Suvrat Raju

High Energy Physics - Theory · Submitted 28 Oct 2005 · 57 references

Pith's verdict: The paper that made the 4d superconformal index a standard tool; the construction and the N=4 matching hold up, with one technical gap in the 'captures all information' argument.

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arXiv IDhep-th/0510251 (version 4)

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CitationJuan Maldacena, Justin Kinney, Shiraz Minwalla, Suvrat Raju. "An Index for 4 dimensional Super Conformal Theories." arXiv:hep-th/0510251 (2005). https://pith.science/paper/AHRXTGEU

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Editor's note

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This is the paper that turned the superconformal index into a working tool, and it holds up. The construction in sections 2-3 is careful, the N=4 evaluation is exact on both sides, and the authors are unusually straight about what they cannot do. Worth your time, and worth citing as the reference for the index itself rather than for any of the black hole commentary around it. What is genuinely new: an index for arbitrary four-dimensional superconformal algebras, a function of two, three and four continuous variables for N=1,2,4; the structural argument in 3.2-3.3 that the trace captures all group-theoretically protected data; and the exact weak/strong match for N=4. The two sides of that match are computed by different methods, a holonomy matrix integral (4.1) at weak coupling and a Fock-space sum over IIB Kaluza-Klein modes (4.15) at strong coupling, and they agree term by term in the chemical potentials in (4.7). That is a real check, not a fit. Section 6 is a second paper's worth of content: exact chiral ring partition functions, 1/2, 1/4 and 1/8 BPS counting, and a Bose-Einstein phase transition at large N. Section 6.2's protected double-trace operator in the 20 is a nice application, cross-checked against the published non-renormalization theorems. The soft spot is the injectivity step behind the abstract's 'captures all information' claim. Sections 3.2-3.3 argue that each independent index I_L appears in (3.9) multiplied by a distinct SU(2,1|m-1) character, so it can be read off. Distinct is not the same as linearly independent, and for supergroups atypical supercharacters can vanish identically. The paper does not check non-vanishing for the quantum numbers that actually arise. This is a technical gap in the conceptual claim, not in the N=4 results, which do not depend on it, and the nontrivial product formula (4.7) shows the characters are non-vanishing at least where N=4 uses them. Flag it, do not hold the paper for it. Two smaller things, both acknowledged by the authors: the giant graviton counting in 5.4 is admittedly not a controlled derivation, and the black hole comparison in 5.3 is loose, with the two-parameter versus three-charge mismatch left unresolved. Send it to referees. This is the reference for the index.

Referee report

Significance

This is an important and carefully executed paper. The weak/strong matching of the index is a genuine, non-trivial check of AdS/CFT in the BPS sector, computed by two independent methods (a weak-coupling holonomy integral and a strong-coupling Fock-space sum over the free supergravity spectrum) with no fitting between them; the agreement is term by term in the chemical potentials. The representation-theoretic framework of Sections 2 and 3, including the independent re-derivation of the null-vector structure in Appendix B.2, is a useful tool for general 4d SCFTs. The chiral-ring partition functions and the identification of the Bose-Einstein phase transition are of independent interest, and the discussion of why the index does not reproduce black-hole entropy is a valuable clarification.

Major objections (1)

[§3.2–3.3, Eqs. (3.9), (3.15); abstract:s1] The abstract's central conceptual claim, that the index 'captures all information ... about protected short representations' (abstract:s1), rests on the decomposition (3.9) and (3.15), in which each independent index I_L (2.18) and I_R (2.19) appears multiplied by a subalgebra supercharacter χ_sub. The paper correctly notes that the map from representations to subalgebra characters is many-to-one and defines I_L as the alternating sum that makes the coefficient well defined. The remaining step, however, requires the χ_sub for distinct (j2, r̂, M, R_j) to be linearly independent as functions of the chemical potentials. For ordinary groups this follows from distinctness of highest weights, but the χ_sub here are supercharacters of short (atypical) representations of SU(2,1|m-1), and atypical supercharacters can vanish identically. The paper does not verify non-vanishing. A concrete check would be to evaluate χ_sub[⃗c_0] at generic chemical potentials for the representations with j1=0, r=r̂, R1=M and confirm it is a nonzero rational function; Appendix C does this explicitly for the N=4 case (Table 3), but the general-m argument in §3.2–3.3 does not. If any χ_sub vanishes for quantum numbers that arise, the corresponding I_L is not recoverable from I_W and the 'captures all information' claim fails for that index. This does not affect the concrete N=4 weak/strong matching, which is protected by the index's invariance, but it is load-bearing for the abstract's main conceptual claim and should be addressed with a short argument or an explicit caveat.

Minor objections (6)

[§5.4, Eq. (5.33) and footnote 17] The authors acknowledge in footnote 17 that the giant-graviton derivation of the small-black-hole entropy is not controlled, since the momentum energy is comparable to the brane tension and no parameter can be adjusted. The statement that 'all factors work bang on' should therefore be presented explicitly as a heuristic numerical coincidence rather than a derivation; the text already gestures at this, but the phrasing could be sharpened.
[§5.3, Eqs. (5.25), (5.26)] The comparison between the free-field cohomological partition function and the supersymmetric black holes yields ratios 1.29 and 0.35, which the authors describe as qualitative agreement. This is appropriately hedged, but the reader would benefit from a sentence stating clearly which features (scaling with N, temperature dependence) are matched and which are not, so that the 'qualitative but not exact' characterization in abstract:s6 is unambiguous.
[§4.1, Eq. (5.13) reference] The text refers to Eq. (5.13) for the single-particle partition function, but the displayed equation in the source is numbered (5.12); please check equation numbering consistency in this region.
[Table 2] The row listing '∂+−ψ0,+;+++ = 0' is described as the single equation of motion modulo which letters are counted; it would help to state explicitly that this is the relation used to eliminate one letter, so that the counting in (4.2) is transparent.
[Throughout] There are numerous typographical and OCR-style errors in the manuscript (e.g., 'masssless' in the abstract, 'fo ur', 'representat ions', 'Inde x', 'anihillates' in §6.1). A careful copy-edit is warranted.
[§2.5, Eq. (B.3)] For m=1 the sums in (B.3) run over infinitely many representations and the paper notes they 'could diverge'; it would be useful to state explicitly whether the N=1 indices are well defined as formal series or require regularization.

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The paper

The paper claims

A single supersymmetric trace formula is claimed to capture every protected short multiplet of four-dimensional superconformal field theories, and for $N=4$ Yang-Mills it matches the free supergravity spectrum on $AdS_5$ exactly.

The reading

Four-dimensional superconformal field theories contain special 'short' multiplets whose dimension is fixed by their charges, and the question this paper takes up is how much of that protected structure can be read off from one counting function. The authors define an index $I_W = (-1)^F e^{M}$ traced over states on $S^3$ times time that are annihilated by a chosen supercharge, which makes the trace independent of the coupling and of the auxiliary parameter $2{S,Q} = H - 2J_1 - 2J_2 - r$ that plays the role of a temperature. They then argue that this trace is not merely a convenient invariant: decomposing it into characters of the residual superalgebra $SU(2,1|m-1)$ shows that each independent short-multiplet index appears multiplied by a distinct character, so the trace carries all the protected information group theory alone can supply. For $N=4$ Yang-Mills the index is a function of four continuous variables, and the authors evaluate it twice, once as a matrix integral over the gauge holonomy and once as a gas of free massless type IIB states on $AdS_5$ times $S^5$, finding the two answers coincide exactly at large $N$ and small charges.

What carries the argument

The load-bearing object is the operator $2{S,Q} = H - 2J_1 - 2J_2 - r$, which is positive semi-definite on every unitary representation, so states with $2{S,Q} = 0$ are annihilated by both $Q$ and $S$ and are the only states the index sees. Because $Q$ and $S$ commute with the subalgebra $SU(2,1|m-1)$ spanned by the Cartan elements (3.4), the index can be expanded in characters of that subalgebra, and the coefficients are exactly the indices $I_L$ and $I_R$ of (2.18) and (2.19). The second piece of machinery is the single-letter index $f$ over the letters of the $N=4$ theory, whose factorized form (4.3) is what makes the holonomy integral (4.1) a Gaussian saddle point and produces the product formula (4.7); the same product emerges from the Fock-space exponentiation of the supergraviton characters $S_n$ tabulated in Appendix C.

Extended reading notes

Core claim

The paper's claim is that the trace $I_W = (-1)^F e^{M}$ over states with $2{S,Q} = H - 2J_1 - 2J_2 - r = 0$ is a complete bookkeeping device for protected short representations of any four-dimensional superconformal algebra. Completeness is the substantive part: the authors show that on a $c$-type short multiplet the index evaluates to a single irreducible character of the commuting subalgebra $SU(2,1|m-1)$, with the highest weight given explicitly in (3.7), and that different short multiplets contributing to the same index $I_L$ (2.18) all produce the same subalgebra character up to a sign $(-1)^p$. That is what makes the decomposition (3.9) injective and lets the trace stand in for the full list of protected multiplet counts. The concrete payoff is in $N=4$ Yang-Mills: the single-letter index factorizes as $1-f = (1-t^2/w)(1-t^2 w/v)(1-t^2 v)(1-t^3 y)(1-t^3/y)$, the large-$N$ index becomes the infinite product (4.7), and summing the same quantity over the Kaluza-Klein tower of IIB supergravity on $AdS_5$ times $S^5$ reproduces it term by term. The paper also reports exact partition functions for $1/2$, $1/4$ and $1/8$ BPS chiral-ring states, and uses the index to show that four of five double-trace operators of the form (6.9) are protected while the fifth pairs with $O' = tr[X^2]tr[X[Y,Z]]$ into a long multiplet.

Load-bearing premise

The completeness claim rests on the assertion that each independent short-multiplet index appears in the trace multiplied by a distinct character of the commuting superalgebra, so that no two different combinations of protected multiplet counts can produce the same trace; if that map is not injective, the index would lose protected information even while the $N=4$ computations still agreed.

Editorial extensions

If this is right

The index gives a BPS-sector check of AdS/CFT stronger than matching chiral primary operators: the entire single-particle Kaluza-Klein tower of IIB supergravity on $AdS_5$ times $S^5$ is reproduced term by term in the chemical potentials.
Because the index never deconfines and stays independent of $N$ at all chemical potentials, it cannot be used to count $AdS_5$ black hole microstates; any weak-coupling derivation of that entropy must work with the signed partition function rather than the index.
The chiral-ring partition functions (6.3), (6.4) and (6.7) give exact counts of $1/8$, $1/4$ and $1/2$ BPS operators as $N$ particles in harmonic oscillator potentials, with a second-order Bose-Einstein condensation transition at $\tilde\beta_c^2 = \pi^2/6$ in the $1/4$ BPS case.
The index constrains operator mixing without any dynamical input: it identifies which double-trace operators in a given charge sector are protected and which must combine into long multiplets.

Reading between the lines

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

The character-decomposition argument is stated for general $m$ and the authors note that counterparts exist in $d=3,5,6$; carrying it out there would give protected spectra for ABJM-type and six-dimensional theories on the same footing, and the authors flag this as unfinished.
The discrepancy between the index and the signed partition function is the whole story of Appendix D: the index is a Poisson-resummed, sign-cancelled shadow of the partition function, so a genuine microstate count would need an extra commuting charge that resolves the cancelling pairs rather than a better index.
The giant-graviton counting (5.31) to (5.33) reproduces $S = 2\pi\sqrt{2}\,q^{3/2}/N$ with all factors landing, but the authors themselves note that the oscillation energy is comparable to the brane tension; a check at finite $q/N$ or with a second independent charge turned on would test whether the D-brane picture survives beyond the formal match.

Original abstract

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.

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, 6,423 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.96 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.

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	We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time.	contribution 0.99	0.96	0.22	asserted 1.00
s1	Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories.	contribution 0.40	0.83	0.34	asserted 0.92
s2	In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables.	result 0.86	0.74	0.08	asserted 1.00
s3	We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges.	result 0.62	0.96	0.19	asserted 1.00
s4	Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory.	interpretation 0.45	0.87	0.14	asserted 1.00
s5	We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons.	result 0.51	0.34	0.03	hedged possibility 1.00
s6	For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory.	result 0.95	0.93	0.07	asserted 0.98
s7	In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.	contribution 1.00	0.95	0.06	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.84 · evidence from proof or derivation 0.91.

What was examined, and what was not

sources read

arXiv listing abstract v4

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

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hep-th 2018-12 accept novelty 7.0 of 10

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See all 220 Pith citations

How later papers used it

482 later papers cite it

Evidence: substantial. 473 of the citing papers share no author with it, and 90 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 1,053 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

12 later papers by other authors are listed below: 2 built on it, 7 used its method or tool, 1 used its data or values and 2 compared their own results with it.

Builds on it 2 of 4 papers with this label

Made a small extension of this paper to probe the deconfinement transition from the index.

Comments on deconfinement in AdS/CFT (2018) · 1.00 · paraphrased: the licence does not allow quoting
Generalized to arbitrary n_0 the effective action studied in this paper for the case when the chemical potentials of the three R-charges are equal.

The asymptotic growth of states of the 4d N=1 superconformal index (2019) · 0.99 · paraphrased: the licence does not allow quoting

Uses its method or tool 7 of 64 papers with this label

Used the 4d supersymmetric index of this paper in its argument.

Gapped Chiral Fermions (2020) · 1.00 · paraphrased: the licence does not allow quoting
Said its computational techniques were inspired by another work and this paper.

An Index for Quantum Integrability (2019) · 1.00 · paraphrased: the licence does not allow quoting
Obtained its multi-particle index by using the effective matrix integration of this paper and other works.

An Index for Non-relativistic Superconformal Field Theories (2008) · 1.00 · paraphrased: the licence does not allow quoting
Used the superconformal index of this paper as a protected quantity to study the AdS/CFT correspondence for finite N.

Finite $N$ corrections to the superconformal index of toric quiver gauge theories (2019) · 0.81 · paraphrased: the licence does not allow quoting
We use the superconformal index [ref] [equation] to express the BPS spectrum concisely, where $p_i$ are Cartan generators of $G$.

Holographic index calculation for Argyres-Douglas and Minahan-Nemeschansky theories (2021) · Introduction · 0.91
We can compute the superconformal index [ref] both for S-gluing and $Φ$-gluing and we find the following result: say for $N=2$ and genus $g$ building the surface from $2g-2$ three punctured spheres, S: 1+q p(3g-3+(g-1)(1+99+45u^2+45u^-2))+⋯ Φ: 1+q p(3g-3+(g-1)(1+99)+(g-1+2g-2))45u^-2+(g-1-2g+2)45u^2))+⋯ , which is consistent with the S-gluing having flux zero and $Φ$-gluing having flux $1-g$ [ref] .[We use the standard notations for the index [ref] .

Star shaped quivers in four dimensions (2023) · Introduction · 0.82
Employed the method given in this paper to determine the index of single gauge-invariant operators.

Superconformal index of N=3 orientifold theories (2016) · 0.88 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 6 papers with this label

We use Table 2 from [ref] to identify the contributing single-letters and their charges.

Fermionic trace relations and supersymmetric indices at finite $N$ (2026) · Analysis and computation of limits of $𝒩=4$ index · 1.00

Compares with it 2 of 27 papers with this label

The final 1-loop determinant looks vaguely similar[We thank Francesco Benini for pointing our attention to the similarity.] to the multi-graviton partition function of [ref] , $_∞= ∏_k=1^∞(1-q^k)^2/(1-y_1^k)(1-y_2^k)(1-y_3^k)$, where $y_a = e^2πi Δ_1, q = e^2πi τ$, but with the modular transformed fugacities and with a different power of the denominator.

The SUSY Index Beyond the Cardy Limit (2022) · Introduction · 0.99
Contrasted its own phase transition, even in a subsector discarding many states, with this paper's indices, which do not undergo any.

On instantons as Kaluza-Klein modes of M5-branes (2011) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

462 arXiv papers cite this in 975 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 · 539 sentences without a confident label

Contests it 1 paper

However, the index defined in [ref] and some of its generalizations [ref] were found to behave as $𝒪(1)$ in the large $N$ limit, thus failing to account for the correct $𝒪(N^2)$ behaviour of the black hole entropy.

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS$_{\bf 5}$ black holes · Introduction · contest 0.85

Builds on it 3 papers

This is the generalization to arbitrary $n_0$ of the effective action studied in [ref] in the case when the chemical potentials of the three R-charges are equal.

The asymptotic growth of states of the 4d N=1 superconformal index · The large-$N$ saddle points of the superconformal index · 0.99
In this paper, we will compute the three-dimensional version of the index of [ref] , (x,{y_i}) = [(-1)^F x^_0+j y_1^h_2 ⋯y_[/2]-1^h_[/2]] .

Superconformal Indices for Orbifold Chern-Simons Theories · Superconformal index in three dimensions · 0.82
This method is a generalization of the work of [ref] to type $E$ theories.

Tinkertoys for the E7 Theory · Cataloging fixtures using the superconformal index · 0.98

Uses its method or tool 59 papers

In this paper we refine the spectral analysis by combining the supersymmetric indices [ref] with the supersymmetric zeta functions and the supersymmetric determinants recently introduced in [ref] .

Holographic spectral functions for Sasaki-Einstein 5-manifolds · Introduction and conclusions · 0.86
To determine the global symmetry group and number of free hypermultiplets for each of these fixtures, we use the superconformal index [ref] .

Tinkertoys for the $E_6$ Theory · Cataloguing fixtures using the superconformal index · 1.00
The tool we will use to make such a statement is the supersymmetric index [ref] .

Curious patterns of IR symmetry enhancement · Introduction · 1.00

Uses its data or values 6 papers

The entropy at very small chemical potential $β$ with conformal dimension $Δ= J∼N^2$ is [ref] [It is well known that states with $Δ∼(1)$ correspond to perturbative gravitons, those with $Δ∼(N)$ to (dual) giant gravitons and those with $Δ∼(N^2)$ to small black holes with suitable gravitational description.] [equation] This result captures the large temperature behavior of N harmonic oscillators plus an $1/N!$ statistical factor.

Small Black holes vs horizonless solutions in AdS · Half-BPS sector in $=4$ SYM · 0.80
The partition function of these $1/8$-BPS operators is [ref] Z^1/8-BPS_N=∏^∞_m,n,r=0(1-pzq_1^2m+1q_2^2n+1q_3^2r+1)(1-pz^-1q_1^2m+1q_2^2n+1q_3^2r+1)/(1-pq_1^2mq_2^2nq_3^2r)(1-pq_1^2m+2q_2^2n+2q_3^2r+2)|_p^N , where $z$ and $q_i$ are the fugacities of the $SU(2)_R⊂SO(4)$ rotation symmetry and the $SU(3)⊂SU(4)$ R-symmetry.

Holographic covering and the fortuity of black holes · $=4$ SYM and the deformation quantization of LLM geometries · 0.84
Such a list of fields and their quantum numbers is provided by [ref] .

Exact Degeneracy of Casimir Energy for $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory on ADE Singularities and S-Duality · Analysis of Supersymmetry · 0.80

Compares with it 26 papers

It turns out that $Z_gravitons$ does not agree with the result from free SYM theory [ref] .

Supergravitons from one loop perturbative N=4 SYM · Supergraviton partition function · 0.90
We provide one such estimate by comparing the Cardy limit entropy of the index [ref] and that of the classical cohomologies refined by a bonus $U(1)$ symmetry [ref] .

Quantum black hole cohomologies · Introduction and discussions · 0.80
As a result, if the upward-flow cycle from the $t_±$ saddle has non-trivial intersection with the defining contour $C_t$, the corresponding leading-order semiclassical contribution to $ℐ_n,n'$ is [equation] Using the standard AdS$_5$/CFT$_4$ normalization $N^2=π/(2G_5)$, [ref] takes the form [equation] which agrees with the so-called unshifted black-hole saddle of [ref] .

Superconformal indices and black hole saddles · The case $2τ_n-3Δ_n'=1.$ · 0.93

Cites it as support 1 paper

All marginal $=2$ preserving deformations must be exactly marginal, because the chiral $LḆ_1[0;0]^(0 ; 4)_2$ multiplet containing the marginal deformation is absolutely protected: there is no recombination rule that allows it to pair up with other multiplets into a long multiplet (see for instance [ref] ).

Deformations of Superconformal Theories · $d=4$, $=2$ · 0.97

Cites it as background 250 papers

This has been considered in [ref] .

Supergravitons from one loop perturbative N=4 SYM · Supergraviton partition function · 0.95
These states are counted (with sign) by the superconformal index [ref] , and one would expect that the contribution from black holes saturates it at large $N$.

Superconformal indices at large $N$ and the entropy of AdS$_5$ $\times$ SE$_5$ black holes · Introduction · 0.84
The superconformal index, defined and studied in [ref] , see [ref] for a review, is an effective tool for studying 4d $𝒩=1$ SCFTs.

Kaluza-Klein Spectroscopy for the Leigh-Strassler SCFT · The LS superconformal index · 0.88

Discussion

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