The Large N Limit of ${\cal N} =2,1 $ Field Theories from Threebranes in F-theory

Ansar Fayyazuddin; Juan Maldacena; Ofer Aharony

REVIEW

The Large N Limit of ${\cal N} =2,1 $ Field Theories from Threebranes in F-theory

Ofer Aharony, Ansar Fayyazuddin, Juan Maldacena

High Energy Physics - Theory · Submitted 18 Jun 1998 · 36 references

Pith's verdict: A solid early AdS/CFT paper: the fractional-dimension trick and the 7-brane KK sector are the real contributions, and the D4 'exact agreement' is a genuine but narrower check than the wording implies.

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arXiv IDhep-th/9806159 (version 3)

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CitationAnsar Fayyazuddin, Juan Maldacena, Ofer Aharony. "The Large N Limit of ${\cal N} =2,1 $ Field Theories from Threebranes in F-theory." arXiv:hep-th/9806159 (1998). https://pith.science/paper/INK2DGDD

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Worth your time, with one caveat about how much weight the headline claim can bear. The genuinely new things here are (a) the shifted angular momentum m = m-tilde/(1 - alpha/2) on the alpha-deformed sphere, which gives fractional dimensions at the Argyres-Douglas points H0, H1, H2 where no orientifold description exists, and (b) the observation that the wrapped 7-brane's KK modes on S3 supply the G-charged chiral primaries. Both are clean and reusable. The check against the Coulomb-branch dimension 1/(1 - alpha/2) from Argyres-Plesser-Seiberg-Witten is an external check, not a restatement, and it lands. The remark that fractional dimensions force the multiple cover of AdS5 is a nice conceptual point that people quote for good reason. Section 6's ansatz, f^{-1/2} dx_parallel^2 + f^{1/2} g_ij dx^i dx^j with the 5-form tied to df, reducing everything to a Laplace equation on the 7-brane metric, is the part I expect to see reused; the observation that the string-frame curvature blows up at distances growing like e^N in the asymptotically free case is a good one and is consistent with the field theory running. On the D4 comparison: the stress-test note is right that the dimensions are automatic once the SU(2)_R x U(1)_R representations match, since both sides use Delta = 2j + R/2. But the representation match itself, (k+2,k)_0 against q Y^{k-1} q, is not trivial, and the field theory side is the strongly coupled SCFT, so it is a real check. What is softer is the completeness half: the paper says 'it is slightly less trivial to show that these are the only chiral primary fields' and then argues by superpotential descendants with loose notation. That is a sketch, and the word 'exact' is doing more work than the argument supports. It is a modest gap, not a load-bearing flaw, but it is the thing to press on. Sections 5 and 6 are openly sketches and the authors say so. For anyone working on AdS/CFT spectra of N=2 theories or on 3-branes in F-theory backgrounds, this is required reading. Send it out.

Referee report

Significance

This is an early and influential application of the Maldacena conjecture to theories with matter in the fundamental representation and to non-orbifold singularities, where no perturbative orientifold description exists. The identification of fractional conformal dimensions at Argyres-Douglas points with shifted spherical harmonics, and the recognition that the wrapped 7-brane provides a distinct Kaluza-Klein sector of G-charged chiral primaries, are both durable structural results. The D4 comparison is a genuine independent check: the field-theory operator count is performed without reference to the gravity side, so the agreement is not a restatement of the input. The general solution of Section 6, reducing the backreaction problem to a single Laplace equation, is a useful template that has been taken up in later work on non-conformal holography.

Major objections (4)

[§4, completeness of the G-charged spectrum] The claim that the Kaluza-Klein modes of the wrapped 7-brane 'will be all the chiral primaries charged under the global symmetry group G which remain at finite dimension in the large N limit' rests on identifying the worldvolume theory on the 7-branes with pure 8d N=1 SYM of group G, with no additional light states localized at the singularity. For D4 this is a perturbative SO(8) theory and the identification is controlled. For E6, E7 and E8 the paper itself notes that 'gs is of order one', so the 8d theory is strongly coupled and the free Kaluza-Klein tower is an F-theory assumption rather than a derived fact. The paper should state this distinction explicitly, so that the D4 comparison is presented as a check and the E_n spectra as conditional predictions.
[§4, D4 field-theory comparison] The 'exact agreement' claim rests on the assertion that the operators q Y^{k-1} q exhaust the SO(8)-charged chiral primaries. The supporting argument occupies three sentences: 'Any product of X with q turns out to be a descendant because of the W = qXq superpotential. Similarly, any anti-symmetric combination of Y's is a descendant because of the W = YXY piece of the superpotential.' Since this completeness step is load-bearing for the central check, it should be expanded: which F-term relations are used, why fermion bilinears in the quark multiplets cannot generate additional chiral primaries, and how the traceless part of the antisymmetric discussed in footnote 5 enters the counting. As written, the agreement is a representation match plus an asserted completeness.
[§6, Eqs. (6.4)-(6.6)] The statement that the ansatz 'together with (6.6), guarantees that it will also satisfy the equations of motion' is asserted rather than shown. The warp factor f^{1/2} multiplies the transverse 7-brane metric, so the 7-brane background's own equations are modified, and the dilaton is taken over unchanged from the 7-brane solution. A short explicit statement of which supersymmetry variations were checked, and why the dilaton equation is unaffected by the 3-brane source, would strengthen the central result of this section. The boundary condition f→0 at infinity (decoupling limit) versus f→1 (standard D3+7-brane solution) should also be stated once with the precise limit taken.
[§3, validation of the shifted-spectrum method] The claim that the shifted-spectrum method reproduces the orbifold projection for α = 1, 4/3, 3/2 and 5/3 is exhibited explicitly only for a single massless scalar at α = 1, followed by 'The same comparison works for all the other fields as well.' Because the method is then applied to the Argyres-Douglas cases, where no independent field-theory check exists, the validation should be commensurate with the use: a general argument that the hypergeometric equation is insensitive to the shift, or a short table for a few representative fields at one or two values of α, would close the gap.

Minor objections (8)

[§3, after Eq. (3.2)] The sentence 'For N = 1, the field with m̃ = 1 can be identified with the standard coordinate u on the Coulomb branch' uses N, which throughout denotes the number of D3-branes; presumably this should read 'For m̃ = 1'. The notation should be disambiguated.
[§4, Eq. (4.1)] In the equation of motion displayed as Eq. (4.1), the index A appears both as the AdS vector index on the left-hand side and as an internal index inside the epsilon contraction; the indices should be made consistent so that the contraction with F^{(5)} is well defined.
[§2, after Eq. (2.1)] The values of α are typeset as '13, 12, 23, 1, 43, 32, 53'; these should be fractions. It would also help to record the corresponding periods 2π(1-α/2) = 5π/3, 3π/2, 4π/3, π, 2π/3, π/2, π/3, since the orbifold cases are exactly those with period 2π/k.
[§4, footnote 5] The notation N(2N-1) for the two-index antisymmetric tensor of USp(2N) is nonstandard; it should be identified as such, and the decomposition into (N(2N-1)-1) + 1 should be stated in words.
[§5.2] The phrase 'one such multiplet for every possible value of the momentum along the S1, up to infinity in the large N limit' is unclear: the Kaluza-Klein tower is infinite independently of N, and the large-N statement concerns the range over which these states remain in the spectrum. Rewording would help.
[§3, paragraph after Eq. (3.2)] The assertion that fractional dimensions force consideration of the multiple cover of AdS5 deserves one clarifying sentence on how the boundary theory is affected, particularly since for the H_n cases the period 2π(1-α/2) is not of the form 2π/k.
[§6.2] The connection between the c|z̃|² term in the metric expansion and the dimension-five operator in the 6 of SO(6) is stated but not shown; a sentence explaining why the first derivative of the dilaton dominates over the curvature-squared correction would make the claim checkable.
[§6.3, Eq. (6.13)] The sum over images is asserted to give a single-valued f on the z-plane; the normalization relative to the source term (2π)^4 N in Eq. (6.6) should be checked and stated, and the remark that the H_n cases yield 'several groups of branes in the physical z space' needs explanation.

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The paper

The paper claims

D3-branes at F-theory singularities yield a computable large-N chiral spectrum.

The reading

The paper asks whether the large-$N$ limit of four-dimensional gauge theories living on D3-branes near F-theory seven-brane singularities can be read off from their dual geometry, including the operators charged under the exceptional global symmetries. It computes the chiral-primary spectrum by expanding bulk supergravity fields on an $S^5$ whose angular periodicity is deformed by the singularity, and by adding the Kaluza-Klein modes of the wrapped seven-branes. The payoff is a concrete dictionary: at Argyres-Douglas points the Coulomb-branch coordinate has fractional dimension, and for the $D_4$ singularity the predicted spectrum matches the $USp(2N)$ gauge theory with an antisymmetric and four fundamental hypermultiplets at large $N$. The paper also sets up deformations away from the conformal point, reducing the backreacted 3-brane geometry to a Laplace equation, though it does not solve that equation in general.

What carries the argument

The load-bearing device is a harmonic expansion on a compact space that is metrically $S^5$ but has a deformed periodicity in one angular direction, $varphi sim varphi + 2pi(1-alpha/2)$. Bulk fields therefore carry shifted angular momentum $m=tilde m/(1-alpha/2)$, so the usual $S^5$ Laplacian eigenvalue $k(k+4)$ is retained while the dimension $Delta=k+4$ (or $Delta=k$ for the special scalar) becomes fractional. On the seven-brane side, the $7+1$-dimensional $N=1$ vector multiplet is reduced on $S^3$; its scalar and vector spherical harmonics fill short multiplets whose dimensions follow $Delta=2j+R/2$. For the backreacted 3-brane solution, the metric ansatz $ds^2=f^{-1/2}dx_parallel^2+f^{1/2}g_{ij}dx^idx^j$ turns the Einstein equations into $frac{1}{sqrt g}partial_i(sqrt g,g^{ij}partial_j f)=-(2pi)^4Ndelta^6(x-x_0)/sqrt g$.

Extended reading notes

Core claim

The central claim is that the large-$N$ spectrum of chiral primary operators in these $N=2$ and $N=1$ superconformal theories is captured by two sectors of the dual string geometry: bulk supergravity modes on the deformed $S^5$, and Kaluza-Klein modes of seven-branes wrapped on an $S^3$. For the $D_4$ singularity the authors compare the resulting $SO(8)$-charged spectrum with the $USp(2N)$ gauge theory and report agreement at large $N$. They also find operators with fractional conformal dimensions at the $H_0,H_1,H_2$ Argyres-Douglas points, and they argue that the seven-brane modes exhaust the $G$-charged chiral primaries that stay at finite dimension. The deformation analysis is a separate contribution: a general 3-brane in a 7-brane background is reduced to a single harmonic function obeying a Laplace equation.

Load-bearing premise

The low-energy theory on each wrapped seven-brane is exactly the $7+1$-dimensional $N=1$ super Yang-Mills theory with gauge group $G$, and its Kaluza-Klein modes on $S^3$ exhaust all $G$-charged chiral primaries that remain at finite dimension; the paper argues this completeness from supersymmetry rather than by expanding the seven-brane action.

Editorial extensions

If this is right

At the $H_0$, $H_1$, and $H_2$ Argyres-Douglas points, the Coulomb-branch coordinate has dimension $6/5$, $4/3$, and $3/2$, respectively, and higher powers fill symmetric products at large $N$.
Each wrapped seven-brane contributes an infinite tower of $G$-charged chiral primaries with dimensions $k+1$, starting with the global symmetry current multiplet.
For $D_4$, the $SO(8)$-charged chiral-primary count agrees with the $USp(2N)$ theory built from two quarks and antisymmetric hypermultiplet fields.
Intersecting seven-branes give $N=1$ theories with shifted $R$-charges and extra multiplets localized on the intersection, including Kaluza-Klein modes of a six-dimensional tensor multiplet on an $S^1$.
The general 3-brane-in-7-brane ansatz gives a large-$N$ gravity description of non-conformal theories; in an asymptotically free case the string-frame curvature grows at distances exponential in $N$, mirroring logarithmic running.

Reading between the lines

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

If the seven-brane Kaluza-Klein tower is complete, the same construction gives testable spectra for the $E_6,E_7,E_8$ theories that are not reachable by a weakly coupled Lagrangian; a string-theory or flow-based count could confirm or break the prediction.
The fractional dimensions suggest that the dual geometry should be treated on a multiple cover of AdS$_5$; this could show up as shifted level spacings in the spectrum rather than as a new continuous parameter.
The Laplace-equation reduction is a practical route to numerical backgrounds for 3-branes away from conformal points, including the logarithmic running of an asymptotically free gauge coupling.
The $D_4$ agreement indicates that fundamental matter in the large-$N$ limit is captured by wrapped-brane modes, which suggests a broader dictionary between seven-brane Kaluza-Klein harmonics and gauge-invariant operators built from quarks.

Original abstract

We consider field theories arising from a large number of D3-branes near singularities in F-theory. We study the theories at various conformal points, and compute, using their conjectured string theory duals, their large $N$ spectrum of chiral primary operators. This includes, as expected, operators of fractional conformal dimensions for the theory at Argyres-Douglas points. Additional operators, which are charged under the (sometimes exceptional) global symmetries of these theories, come from the 7-branes. In the case of a $D_4$ singularity we compare our results with field theory and find agreement for large $N$. Finally, we consider deformations away from the conformal points, which involve finding new supergravity solutions for the geometry produced by the 3-branes in the 7-brane background. We also discuss 3-branes in a general background.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.91 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We consider field theories arising from a large number of D3-branes near singularities in F-theory. We study the theories at various conformal points, and compute, using their conjectured string theory duals, their large $N$ spectrum of chiral primary operators. This includes, as expected, operators of fractional conformal dimensions for the theory at Argyres-Douglas points. Additional operators, which are charged under the (sometimes exceptional) global symmetries of these theories, come from the 7-branes. In the case of a $D_4$ singularity we compare our results with field theory and find agreement for large $N$. Finally, we consider deformations away from the conformal points, which involve finding new supergravity solutions for the geometry produced by the 3-branes in the 7-brane background. We also discuss 3-branes in a general background.

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 consider field theories arising from a large number of D3-branes near singularities in F-theory.	contribution 0.60	0.70	0.05	asserted 0.87
s1	We study the theories at various conformal points, and compute, using their conjectured string theory duals, their large $N$ spectrum of chiral primary operators.	contribution 0.92	0.95	0.13	asserted 0.93
s2	This includes, as expected, operators of fractional conformal dimensions for the theory at Argyres-Douglas points.	result 0.92	0.70	0.12	asserted 0.94
s3	Additional operators, which are charged under the (sometimes exceptional) global symmetries of these theories, come from the 7-branes.	result 0.95	0.70	0.07	asserted 0.99
s4	In the case of a $D_4$ singularity we compare our results with field theory and find agreement for large $N$.	result 0.92	0.93	0.13	asserted 1.00
s5	Finally, we consider deformations away from the conformal points, which involve finding new supergravity solutions for the geometry produced by the 3-branes in the 7-brane background.	contribution 0.91	0.91	0.06	asserted 0.96
s6	We also discuss 3-branes in a general background.	contribution 0.98	0.80	0.04	asserted 0.84

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.74.

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sources read

arXiv listing abstract v3

not examined

full text
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levels run

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C citations
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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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All tree-level four-point super gluon amplitudes in a broad class of holographic SCFTs with non-maximal supersymmetry are shown to be fixed by superconformal symmetry and constructed explicitly.
Universal Features of BPS Strings in Six-dimensional SCFTs
hep-th 2018-04 conditional novelty 7.0 of 10

A uniform (0,4) sigma-model description of BPS strings in rank-one 6d SCFTs, combined with modularity, fixes the elliptic genera of most such strings and yields new 5d instanton partition functions.
S-folds and 4d N=3 superconformal field theories
hep-th 2016-02 accept novelty 7.0 of 10

Only five variants of N=3-preserving S-folds exist, labeled by (k,ell) = (3,1), (3,3), (4,1), (4,4), (6,1), as shown by matching F-theory discrete torsion against M-theory orbifold charges.
General Argyres-Douglas Theory
hep-th 2012-04 conditional novelty 7.0 of 10

Compactifying the six-dimensional (2,0) A_{N-1} theory on a sphere with irregular singularities yields a classified family of Argyres-Douglas theories whose Seiberg-Witten curves, scaling dimensions, and central charg...
Central charges of N=2 superconformal field theories in four dimensions
hep-th 2008-04 conditional novelty 7.0 of 10

The central charges a and c of a strongly coupled N=2 SCFT are read off from the R-charge of the topological path-integral measure factor A^chi B^sigma, with no holography required.
Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
hep-th 2007-12 accept novelty 7.0 of 10

General R^2 corrections to AdS gravity shift the dual theory's viscosity-to-entropy ratio by a term proportional to c3, and in the N=2 Sp(N) theory with fundamental and antisymmetric matter this pushes the ratio below 1/(4π).
The Pomeron and Gauge/String Duality
hep-th 2006-03 conditional novelty 7.0 of 10

The soft Regge and hard BFKL Pomeron are unified in gauge/string duality as the spectrum of one j-plane Schrödinger operator, with strong-coupling intercept 2 - 2/sqrt(lambda).
Meson Spectroscopy in AdS/CFT with Flavour
hep-th 2003-04 accept novelty 7.0 of 10

The meson spectrum of an N=2 super Yang-Mills theory with fundamental quarks is computed analytically from a D7-brane probe in AdS5 x S5, yielding a discrete spectrum with a mass gap and Regge-like behaviour at large spin.
AdS/CFT Correspondence and Symmetry Breaking
hep-th 1999-05 accept novelty 7.0 of 10

The two admissible quantizations of a light scalar in AdS correspond to two boundary CFTs whose generating functionals are Legendre transforms of each other, and the same dictionary converts metric falloffs into scala...
Bootstrapping Holographic Theories in the Planar Limit
hep-th 2026-09 conditional novelty 6.0 of 10

Bootstrap plus localization, with no integrability input, reproduces single-trace operator dimension bounds that match independent predictions in planar N=4 SYM and in an N=2 open-string dual.
Strong-coupling results in (non-)conformal $\mathcal{N}=2$ theories with fundamental flavors
hep-th 2026-05 unverdicted novelty 6.0 of 10

Localization matrix models yield resummed strong-coupling expressions for observables in N=2 theories with antisymmetric and fundamental matter, using an effective 't Hooft coupling at large N.
Monodromy Relations for String Amplitudes on AdS
hep-th 2025-09 conditional novelty 6.0 of 10

The authors conjecture a set of monodromy relations for the AdS Veneziano amplitude, upgrade the flat-space relations with operators acting on multiple polylogarithms, and verify them against all known curvature corre...
Meson correlators in 4d $\mathcal{N}=2$ SCFTs and hints for 8d structures at weak coupling
hep-th 2024-12 conditional novelty 6.0 of 10

One-loop meson correlators in two N=2 SCFTs resum into generating functions that display hidden 8d conformal structure at weak coupling.
BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
hep-th 2021-06 conditional novelty 6.0 of 10

Color/kinematics duality and the BCJ amplitude relations generalize to anti-de Sitter boundary correlators when Mandelstam invariants are replaced by conformal-generator operators, checked for Yang-Mills at four point...
Holographic duals of 3d S-fold CFTs
hep-th 2018-04 accept novelty 6.0 of 10

A class of non-geometric AdS4 string backgrounds is shown to match the three-sphere partition function of a proposed dual 3d N=4 quiver theory, exactly at finite N and in the large-N gravity limit.
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.
On Exceptional Instanton Strings
hep-th 2016-09 conditional novelty 6.0 of 10

The 2d worldsheet theories of BPS instanton strings in 6d (1,0) SCFTs with simply-laced gauge groups are beta-twisted compactifications of 4d N=2 H_G theories, and their one-instanton elliptic genera are fixed by modularity.
$\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
hep-th 2015-11 conditional novelty 6.0 of 10

A new analytic inequality relating the c-anomaly to the flavor central charge in N=2 superconformal theories excludes a region of parameter space and uniquely fixes a special family of models.
Bootstrapping ${\mathcal N}=2$ chiral correlators
hep-th 2015-10 accept novelty 6.0 of 10

Crossing symmetry plus unitarity, implemented numerically, confines OPE data of N=2 chiral operators, pins one unprotected coefficient of the H0 Argyres-Douglas theory to about 0.5 percent, and rules out chiral-ring r...
Stress-tensor OPE in N=2 Superconformal Theories
hep-th 2015-08 conditional novelty 6.0 of 10

The OPE of two N=2 stress-tensor multiplets is classified, and unitarity of the associated two-dimensional chiral algebra implies c ≥ 11/30 for every interacting N=2 SCFT.
The ${\mathcal N}=2$ superconformal bootstrap
hep-th 2014-12 conditional novelty 6.0 of 10

Crossing symmetry plus superconformal block expansions yields rigorous numerical bounds on central charges, operator dimensions, and OPE coefficients for any four-dimensional N=2 superconformal field theory.
Micromanaging de Sitter holography
hep-th 2010-05 conditional novelty 6.0 of 10

The authors construct three-dimensional de Sitter vacua in string theory whose compact brane construction provides a parametric microscopic account of the Gibbons-Hawking entropy.
A holographic model of deconfinement and chiral symmetry restoration
hep-th 2006-04 accept novelty 6.0 of 10

In the Sakai-Sugimoto holographic model, deconfinement and chiral symmetry restoration coincide only when the quark separation exceeds about 0.97 times the compactification radius; below that, an intermediate deconfin...
Conformal Technicolor
hep-ph 2004-09 conditional novelty 6.0 of 10

Strong small-N conformal field theories with an electroweak order parameter of dimension 1 + epsilon, epsilon of order 1/few, can decouple flavor and keep the S parameter small, at the price of assuming such theories exist.
Holomorphic D7-Branes and Flavored N=1 Gauge Theories
hep-th 2003-11 conditional novelty 6.0 of 10

Holomorphic D7-branes in the warped conifold add quarks to the Klebanov-Strassler cascade, and the resulting three-form flux running shows the duality cascade slowing and potentially stopping in the infrared.
On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections
hep-th 2018-11 accept novelty 5.0 of 10

Pole-skipping persists in holographic theories with R-squared and alpha-prime-cubed R-to-the-fourth gravity corrections, and it predicts a specific finite-coupling shift in the butterfly velocity that an independent s...
Mesons in Gauge/Gravity Duals - A Review
hep-th 2007-11 conditional novelty 3.0 of 10

Probe flavour branes in deformed, non-supersymmetric gravity duals reproduce confinement, a quark condensate, a Goldstone pion-like mode, and meson masses that track quenched lattice data at the ten-percent level.
From gauge-string duality to strong interactions: a Pedestrian's Guide
hep-th 2009-01 accept novelty 2.0 of 10

A pedagogical survey of holographic models of QCD-like gauge theories and their application to quark-gluon plasma physics, with an explicit accounting of what the approach can and cannot yet do.
Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
hep-th 2008-07 accept novelty 1.0 of 10

The review organizes evidence that MHV scattering amplitudes in planar N=4 SYM equal expectation values of null polygonal Wilson loops, with dual conformal symmetry controlling the finite parts.

How later papers used it

97 later papers cite it

Evidence: substantial. 95 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 152 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

2 later papers by other authors are listed below: 1 built on it and 1 compared its own results with it.

Builds on it 1 of 4 papers with this label

Representations with $k=0$ and $k=1$ have special structure and they are denoted in [ref] as follows: [equation] For the analysis of $G=H_n$ we need to extend the range of $k$ [ref] to fractional values.

Holographic index calculation for Argyres-Douglas and Minahan-Nemeschansky theories (2021) · Gravity multiplet · 0.87

Compares with it 1 of 4 papers with this label

Compared the backgrounds found by this paper and another work, which solve the pure supergravity equations of motion without source terms for flavor or color-branes, to its own new solutions.

Comments on the distinction between color- and flavor-branes and new D3-D7 solutions with eight supercharges (2010) · 0.89 · paraphrased: the licence does not allow quoting

How the literature uses it

96 arXiv papers cite this in 152 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 · 81 sentences without a confident label

Builds on it 4 papers

In the orbifold case considered in [ref] the internal space is $S^5_α_G=S^5/_Δ_G$, and the Kaluza-Klein modes in the orbifold are obtained from those in $S^5$ by picking up $_Δ_G$ invariant modes, whose quantum numbers satisfy [equation] The analysis in [ref] was extended in [ref] in two ways: The non-orbifold cases with $G=H_0,H_1,H_2$ were included by allowing fractional values of $Δ_G$ in ([ref]), and fields living on the $7$-brane were taken into account to generate the spectrum of operators transformed non-trivially under $G$.

Holographic index calculation for Argyres-Douglas and Minahan-Nemeschansky theories · Introduction · 0.93
This partially reduces the scarcity of AdS$_d$ “solutions” of F-theory, extending the class of those claimed to exist in [ref] (for $d=5$), [ref] (for $d=3$) and [ref] (for $d=4$) to the case $d=7$.[ Notice however a crucial difference.

AdS$_7$/CFT$_6$ with orientifolds · A formal massive IIA quiver and its dual vacuum · 0.98
This surprising appearance of duals to 4d SCFTs, generalising known constant but non-perturbative $τ$ solutions of [ref] , is welcome and will be studied elsewhere in more detail [ref] .

F-theory and AdS_3/CFT_2 (2,0) · Introduction · 0.81

Uses its method or tool 1 paper

This strategy to obtain the spectrum was used in [ref] , and the analyses led to the following results.

Gluon Scattering in AdS from CFT · Kinematics of four-point functions · 0.87

Uses its data or values 1 paper

To be concrete, the $(1)_R$ 't Hooft anomalies for the 4d $𝒩=2$ SCFTs arising from D3-branes at F-theory singularities are [ref]

Higher-Derivative Corrections and AdS$_5$ Black Holes · Introduction · 0.96

Compares with it 4 papers

Here we will compare the backgrounds found by [ref] - Grana:2001xn [ref] , which solve the pure supergravity equations of motion without any source terms for either flavor or color-branes, to new solutions, found working in the spirit of [ref] solving the system given by $S_IIB + S_flavor$.

Comments on the distinction between color- and flavor-branes and new D3-D7 solutions with eight supercharges · Introduction · 0.89
This is easily done by comparing with the results of [ref] , where the dimensions of these operators at the UV fixed point ($N=4$ SYM coupled to massless $N=2$ matter) were computed.

Towards holographic walking from N=4 super Yang-Mills · A discussion on the dimensions · 0.93
Unlike e.g. the CFT dual in [ref] , the backreaction of this modes on the geometry has not been included, i.e. the background metric is not modified by the presence of the D8-branes.

Introduction to AdS-CFT · Gravity duals · 0.96

Cites it as support 1 paper

Arguments have indeed been presented in [ref] (following earlier work on D7 branes in [ref] ) that no such fully back-reacted solutions corresponding to D7 branes should exist.

Half-BPS supergravity solutions and superalgebras · On the existence of fully back-reacted D7 brane solutions · 0.98

Cites it as background 46 papers

In the simplest holographic setup one considers a small number of D7 branes as probes to $AdS_5 ×S^5$.[See [ref] for further details on the setup.] The world-volume of the D7-branes wraps around $AdS_5$ and an equatorial $S^3$ inside $S^5$.

Single-valuedness of the AdS Veneziano amplitude · Introduction · 0.98
Through the AdS/CFT correspondence, this string theory is dual to a four-dimensional $=2$ SYM theory with gauge group [In this paper we use the notation Sp($N$) to indicate the symplectic group of rank $N$.] Sp($N$), one anti-symmetric hypermultiplet and four fundamental hypermultiplets with an SO(8) flavor symmetry [ref] .

Integrated correlators in a $\mathcal{N}=2$ SYM theory with fundamental flavors: a matrix-model perspective · Introduction and summary of results · 0.88
The prototype is the class of $𝒩=2$ superconformal gauge theories arising from $N$ D3's in the presence of 4 D7's and an $Ω7^-$ plane [ref] .

Unoriented Quivers with Flavour · Conformal theories · 0.95

Discussion

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

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