Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N

Mukund Rangamani; Nathan Seiberg; Sangmin Lee; Shiraz Minwalla

REVIEW

Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N

Sangmin Lee, Shiraz Minwalla, Mukund Rangamani, Nathan Seiberg

High Energy Physics - Theory · Submitted 9 Jun 1998 · 24 references

Pith's verdict: A clean, honest paper: the free-field and supergravity three-point functions really do match, and the λ-independence is properly labeled a conjecture rather than sold as a theorem.

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arXiv IDhep-th/9806074 (version 3)

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CitationMukund Rangamani, Nathan Seiberg, Sangmin Lee, Shiraz Minwalla. "Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N." arXiv:hep-th/9806074 (1998). https://pith.science/paper/RPNA6Z4P

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Editor's note

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The thing to know: the free-field computation of the three-point functions of chiral primary operators (Eq. 2.4) and the supergravity computation (Eq. 4.7) agree exactly, including the full k1,k2,k3 dependence. That k-dependence is the substance here, and it is not something you get for free from a normalization choice. The paper is careful about what it has and has not shown, which is rarer than it should be in this literature. I'd take it seriously and I'd cite it. I'd also send it to referees without hesitation, though I doubt they'd find much beyond polish issues. The weak-coupling side is standard and correct. The strong-coupling side is the real work: they work with equations of motion rather than a covariant action, solve the constraints, diagonalize s and t, do field redefinitions to kill derivative terms, and then fix the overall normalization of the cubic action. That last step is the one soft spot worth naming. The normalization is anchored to the known exact R-current three-point function, which is a descendant of the k=2 operator. That is an external anchor, not a fit to the data being predicted, so it is not circular in the way a quick read might suggest. But it does mean the overall coefficient of Eq. 4.7 rests on assumptions about the true IIB action including surface terms, and the authors say so. The k-dependence is the independent check, and it passes. The λ-independence claim (abstract:s3) is explicitly a conjecture, and the paper is upfront about the finite-N puzzle and even flags the tension with flat-space intuition about three-graviton scattering. That is the kind of honesty I want to see. Two small things. The abstract says 'all' three-point functions, but the body restricts to k≥2; k=1 is a special case and does not affect the central agreement, but the wording is a touch loose. And 'surprisingly' in abstract:s2 is doing some work, given that non-renormalization was already expected from [18,19] and Banks-Green [17]. Neither is a reason to hold the paper back. This is a benchmark paper for anyone working on AdS/CFT correlators or on non-renormalization in N=4. Read it, cite it, and treat the conjecture as a conjecture.

Referee report

Major objections (1)

[Section 3.4, Eqs. (3.17)-(3.23), and Section 4] The determination of the quadratic normalization A_I is the least transparent and most load-bearing step in the strong-coupling calculation. A_I enters the normalized three-point function through the ratio of (4.6) to the 2-point functions (4.5), so its k-dependence is part of the prediction rather than a normalization that cancels; the agreement of (4.7) with (2.4) for all k depends on it. The derivation evaluates the on-shell quadratic action (3.22), which contains higher-derivative terms such as (nabla^lambda nabla^(mu nabla^nu) s^I)^2, as a boundary term; the treatment of surface terms and of higher-derivative boundary contributions should be spelled out explicitly. In addition, Section 3.1 states that the normalization is fixed by comparison with the action of [23] at quadratic order, while Section 4 states that the overall normalization is fixed by matching the exact R-current three-point function. The manuscript should state clearly which step fixes the overall constant and which fixes the relative k-dependence. This is a request for clarification rather than a claim of error: the exact match with (2.4) and the R-current anchor make the result credible, but the derivation as written is difficult to check independently.

Minor objections (7)

[Abstract and Section 3.3] The abstract refers to 'all three-point functions of normalized chiral operators', but Section 3.3 restricts the supergravity analysis to k >= 2. The k = 1 CPO (Tr phi^i, dimension 1) has a vanishing three-point function in free field theory (the alpha_i are half-integers), and it is excluded from the supergravity analysis because the constraint (3.6) cannot be used to eliminate h' for k = 1. A sentence noting that the k = 1 case is trivially zero would make the word 'all' accurate.
[Eq. (4.5)] The factor (k-2)^2 in (4.5) vanishes at k = 2, whereas the limit of (4.3) as k -> 2 is finite. Since the k = 2 case is used to anchor the overall normalization through the R-current three-point function, the manuscript should clarify how the k = 2 limit of the CPO two-point function is taken and confirm that (4.5) is not being evaluated at its removable singularity.
[Section 2, Eqs. (2.2)-(2.4)] The free-field computation is performed for U(N), whose trace includes a U(1) piece. A short sentence noting that the U(1) sector contributes only at subleading order in 1/N for k >= 2, so that (2.2)-(2.4) are unaffected, would preempt a natural question from readers accustomed to working with SU(N).
[Section 3.5, Eqs. (3.36)-(3.38)] The field redefinition that removes the derivative terms from (3.35) is standard, but the manuscript should state explicitly that the induced change in the three-point function is a contact term that vanishes at separated points, so that the correlation function of interest is unaffected.
[Section 3.1, point 3] The statement that nonlinear corrections to the identification of the fields coupling to the operators modify the correlators only by contact terms is correct but is asserted rather than explained. A sentence spelling out the argument (field redefinitions that vanish on shell do not change S-matrix elements, and the corresponding change in the correlator is a contact term) would make this step self-contained.
[Abstract and Section 4, lambda-independence conjecture] The conjecture is appropriately labelled, and the manuscript correctly cites [17] only for the absence of the leading 1/lambda correction. It would strengthen the discussion to state explicitly what would falsify the conjecture, for example a nonzero subleading 1/lambda or 1/N correction, and to note that the two-endpoint agreement does not by itself exclude intermediate-coupling corrections.
[Front matter and references] There are several typographical errors: the email line reads 'rangamni' rather than 'rangamani'; 'supercoformal' appears in Section 4; 'therory' appears in reference [22]; and the spellings 'G¨ unaydin' and 'M¨ uck' should be 'Günaydin' and 'Mück'.

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The paper

The paper claims

The same three-point function comes out at weak and strong coupling in N=4 super Yang-Mills, so the authors conjecture it never depends on the coupling at all.

The reading

In $D=4$, $N=4$ supersymmetric Yang-Mills theory the coupling constant is a free dial, and most quantities turn on it. Chiral primary operators are the exception on the scaling-dimension side: supersymmetry fixes their dimension $k$ in terms of their $SO(6)$ representation, with no coupling anywhere. This paper asks whether their three-point functions are equally rigid. It computes all of them at large $N$ in the two limits where calculation is possible — weak coupling by free-field Wick contractions, strong coupling by Kaluza-Klein supergravity on $AdS_5 times S^5$ — and finds the answers identical, including every factor of $k_1,k_2,k_3$. The authors then conjecture that at large $N$ these three-point functions are exactly independent of the 't Hooft coupling $lambda = g_{YM}^2 N$.

What carries the argument

The load-bearing object is a bulk scalar $s^I$ obtained by diagonalizing the linearized IIB supergravity equations: it is a specific mixture of the trace of the graviton on $S^5$ and the five-form field strength, chosen so that its mass satisfies $m^2 = k(k-4)$ and its equation of motion is $nabla^2 s^I = k(k-4) s^I$, matching the dimension of the charge-$k$ chiral primary. The authors derive the cubic couplings of $s^I$ by pushing the Einstein and self-duality equations to quadratic order, removing derivative terms from the right-hand side by a field redefinition, and reading off a totally symmetric vertex $G_{I_1 I_2 I_3}$. Two ingredients make the comparison possible: the integral identities for triple products of $S^5$ spherical harmonics, which supply the same $langle C_{I_1} C_{I_2} C_{I_3} rangle$ contraction that appears on the free-field side, and the normalization of the quadratic action, which is fixed by matching to the exactly known three-point function of $R$-symmetry currents, themselves descendants of the $k=2$ operator.

Extended reading notes

Core claim

The paper's claim is an exact match between two computations that have no obvious right to agree. At weak coupling, the normalized three-point function of chiral primary operators $O_{I}$ built from $k$ adjoint scalars is $N^{-1} sqrt{k_1 k_2 k_3} langle C_{I_1} C_{I_2} C_{I_3} rangle$ times the standard conformal distance factor, with the $SO(6)$ index contraction carrying all the tensor structure. At strong coupling the same correlator is obtained from a five-dimensional cubic action for the bulk fields dual to these operators, and after fixing the overall normalization it reproduces the identical expression, coefficient for coefficient. Because the two endpoints of the coupling range give the same function of $k_1,k_2,k_3$ and of the 't Hooft coupling, the authors conjecture that at large $N$ the exact answer is coupling-independent. They are explicit that this is a conjecture, supported at strong coupling by the earlier observation that the leading large-$lambda$ result receives no correction at the next order.

Load-bearing premise

The conjecture rests on agreement at two endpoints of the coupling range; nothing in the paper rules out a correction that vanishes at both $lambda to 0$ and $lambda to infinity$ but is nonzero in between.

Editorial extensions

If this is right

The three-point functions of the $R$-symmetry currents and of the stress-energy tensor follow as special cases, reproducing results previously obtained by other routes and confirming the overall normalization of the supergravity calculation.
The same non-renormalization cannot extend to four-point functions: the authors note that four-point functions of these operators do depend on the coupling at next-to-leading order, so the rigidity is specific to the three-point level.
If the stronger finite-$N$ version of the conjecture holds, then the three-graviton coupling in $AdS_5 times S^5$ must itself receive quantum string corrections that depend on $N$, a possibility the authors flag as sitting uneasily with flat-space intuition.
The agreement provides a check of the $AdS$/CFT dictionary at cubic order that is sensitive to the full $k$-dependence of the operators, not merely to a single overall constant.

Reading between the lines

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

Because the free-field and supergravity answers differ only by an overall factor that cancels between the two-point and three-point normalizations, the conjecture can be restated as a statement that one specific cubic vertex in the five-dimensional effective action is not renormalized; that is a sharper target for a symmetry argument than the correlator itself.
A natural stress test is the ratio of three-point functions at different charges, for instance $k=2$ against $k=3$: any coupling-dependent correction that is not uniform across $k$ would show up there even if each individual normalization is uncertain.
The paper's own remark that the finite-$N$ version would force $N$-dependent corrections to three-graviton scattering in $AdS_5 times S^5$ suggests a concrete string-theory calculation: a one-loop correction to that vertex in a curved background with maximal supersymmetry, which is where the two claims would collide.
The result invites a search for a non-renormalization theorem covering three-point functions of chiral primaries directly, rather than inferring rigidity from agreement at two isolated values of the coupling.

Original abstract

We study all three-point functions of normalized chiral operators in D=4, $\mathcal{N}=4$, U(N) supersymmetric Yang-Mills theory in the large $N$ limit. We compute them for small 't Hooft coupling $\lambda=g_{YM}^2N<<1$ using free field theory and at strong coupling $\lambda=g_{YM}^2>>1$ using the $AdS$/CFT correspondence. Surprisingly, we find the same answers in the two limits. We conjecture that at least for large $N$ the exact answers are independent of $\lambda $ .

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The abstract, sentence by sentence

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

We study all three-point functions of normalized chiral operators in D=4, $\mathcal{N}=4$, U(N) supersymmetric Yang-Mills theory in the large $N$ limit. We compute them for small 't Hooft coupling $\lambda=g_{YM}^2N<<1$ using free field theory and at strong coupling $\lambda=g_{YM}^2>>1$ using the $AdS$/CFT correspondence. Surprisingly, we find the same answers in the two limits. We conjecture that at least for large $N$ the exact answers are independent of $\lambda $ .

background contribution method result interpretation main claim

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study all three-point functions of normalized chiral operators in D=4, $\mathcal{N}=4$, U(N) supersymmetric Yang-Mills theory in the large $N$ limit.	contribution 0.99	0.89	0.04	asserted 0.91
s1	We compute them for small 't Hooft coupling $\lambda=g_{YM}^2N<<1$ using free field theory and at strong coupling $\lambda=g_{YM}^2>>1$ using the $AdS$/CFT correspondence.	method 0.95	0.93	0.05	asserted 1.00
s2	Surprisingly, we find the same answers in the two limits.	result 1.00	0.96	0.44	asserted 1.00
s3	We conjecture that at least for large $N$ the exact answers are independent of $\lambda $ .	interpretation 0.97	0.32	0.79	speculative 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.87.

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References

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A ten-dimensional formula for the potential of warped flux compactifications is derived, yielding a slope-dominance criterion for de Sitter vacua and a warping-corrected definition of holomorphic Kahler moduli.
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
hep-th 2004-07 accept novelty 7.0 of 10

The complete one-loop dilatation operator of N=4 super Yang-Mills is fixed by superconformal symmetry, shown to be integrable in the planar limit, and solved by a Bethe ansatz.
The dual of Janus -:- an interface CFT
hep-th 2004-07 accept novelty 7.0 of 10

The Janus supergravity solution is dual to N=4 super Yang-Mills on two half-spaces with different couplings, and a protected vacuum expectation value matches between weak and strong coupling.
Supersymmetric Wilson loops
hep-th 2002-05 conditional novelty 7.0 of 10

Constructs 1/16, 1/8, and 1/4 BPS Wilson loops in N=4 SYM and conjectures that the 1/4 BPS planar loops are not renormalized.
Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
hep-th 2001-12 accept novelty 7.0 of 10

Superconformal symmetry fixes the four point function of chiral primary operators up to one function of two variables, and the paper uses this to write the operator product expansion in terms of complete supermultiplets.
Exact Correlators of Giant Gravitons from dual N=4 SYM
hep-th 2001-11 accept novelty 7.0 of 10

Exact finite-N correlators of half-BPS operators in free N=4 SYM are derived and organized by Young diagrams, yielding a dictionary between diagram shapes and giant graviton states in AdS5 x S5.
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...
Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
hep-th 1999-03 accept novelty 7.0 of 10

The graviton exchange Witten diagram is evaluated for arbitrary scalar operators in AdS(d+1), completing the four-point functions of dilaton and axion marginal operators in N=4 SYM at large N and large coupling.
The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
hep-th 1998-09 conditional novelty 7.0 of 10

At strong coupling the OPE coefficients of small Wilson loops in N=4 SYM scale as sqrt(lambda)/N rather than the weak-coupling lambda^{Delta/2}/N, and spherical Wilson surfaces carry a rigid-string logarithmic divergence.
Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
hep-th 2017-10 conditional novelty 6.5 of 10

Adding SU(N) colour factors to the hexagon tessellation prescription makes it reproduce tree-level four-point functions with two non-protected operators, and enables a torus tessellation that captures the leading 1/N ...
Loop Corrected Supercharges from Holomorphic Anomalies
hep-th 2025-12 conditional novelty 6.0 of 10

The complete one-loop supercharge for 4d Lagrangian SUSY gauge theories is derived in the holomorphic twist, packaged for N=4 SYM as a compact superfield formula.
(Un)solvable Matrix Models for BPS Correlators
hep-th 2025-08 unverdicted novelty 6.0 of 10

Proposes complex matrix models for BPS correlators in N=4 SYM, relating eigenvalue distributions to LLM droplet shapes and enabling computations of one-point functions and three-point correlators via reductions to kno...
Tenfold Way for Holography : AdS/CFT and Beyond
hep-th 2020-09 conditional novelty 6.0 of 10

Real semisimple Lie groups are organized into bulk and boundary spaces using Iwasawa, Bruhat, and Sekiguchi-like decompositions, with the key intertwiners left to a sequel.
All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs
hep-th 2020-06 conditional novelty 6.0 of 10

A new 'maximally R-symmetry violating' limit of holographic Mellin amplitudes determines all tree-level four-point functions of half-BPS operators in maximally supersymmetric CFTs in 3, 4, and 6 dimensions.
Simplicity of AdS Supergravity at One Loop
hep-th 2019-12 conditional novelty 6.0 of 10

A systematic algorithm fixes one-loop Mellin-space holographic four-point correlators in AdS5 x S5 supergravity from tree-level data, producing a closed-form expression for a one-parameter family of correlators.
More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
hep-th 2018-11 accept novelty 6.0 of 10

Bulk-defect correlators on the 1/2-BPS Wilson loop in N=4 SYM are computed exactly at planar order and expressed as contour integrals over Quantum Spectral Curve Q-functions, matching both weak-coupling perturbation t...
On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
hep-th 2017-12 conditional novelty 6.0 of 10

Translating superconformal Ward identities into Mellin space gives a bootstrap that computes holographic four-point functions for 3≤d≤6, including a first result for AdS4×S7.
Holographic Four-Point Functions in the (2, 0) Theory
hep-th 2017-12 conditional novelty 6.0 of 10

New holographic four-point functions for massive Kaluza-Klein modes in AdS7 x S4 are computed from superconformal symmetry and matched to W-infinity chiral algebra correlators.
How to Succeed at Holographic Correlators Without Really Trying
hep-th 2017-10 conditional novelty 6.0 of 10

A single rational Mellin-space formula is conjectured to reproduce every strong-coupling four-point function of half-BPS operators in N=4 super Yang-Mills, and two bootstrap methods reproduce it without evaluating the...
Unmixing Supergravity
hep-th 2017-06 accept novelty 6.0 of 10

The paper resolves the mixing of double-trace operators in the supergravity limit of N=4 super Yang-Mills and gives closed-form anomalous dimensions and three-point functions for a large family of them.
Correlation Functions of Coulomb Branch Operators
hep-th 2016-02 accept novelty 6.0 of 10

Extremal correlation functions of Coulomb branch operators in 4d N=2 SCFTs equal ratios of determinants of derivatives of the deformed four-sphere partition function, and obey an integrable Toda chain system.
On exact correlation functions in SU(N) ${\cal N} = 2$ superconformal QCD
hep-th 2015-08 conditional novelty 6.0 of 10

A no-mixing conjecture for chiral primary correlators in SU(N) N=2 superconformal QCD is proposed and checked to three loops in SU(3) and SU(4), reducing the tt* equations to solvable Toda chains.
Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap
hep-th 2014-12 accept novelty 6.0 of 10

A supercharge-cohomology truncation of crossing symmetry yields exact, theory-independent relations among OPE coefficients in 3d N>=4 SCFTs, and fixes infinitely many three-point functions in the U(2)_2 x U(1)_-2 ABJ theory.
Exact correlation functions in SU(2) N=2 superconformal QCD
hep-th 2014-09 conditional novelty 6.0 of 10

Exact two- and three-point functions of chiral primary operators in SU(2) N=2 superconformal QCD are obtained by solving a semi-infinite Toda chain whose input is the Zamolodchikov metric from localization on the four-sphere.
$tt^*$ equations, localization and exact chiral rings in 4d N=2 SCFTs
hep-th 2014-09 accept novelty 6.0 of 10

Exact all-instanton two- and three-point functions of chiral primaries in SU(2) N=2 superconformal QCD follow from a semi-infinite Toda chain seeded by the S^4 partition function.
Event shapes in N=4 super-Yang-Mills theory
hep-th 2013-09 conditional novelty 6.0 of 10

Event shapes in N=4 super-Yang-Mills reduce to a Mellin-space convolution of the four-point half-BPS correlation function with a coupling-independent detector kernel, verified at one loop and extended to strong coupling.
Correlation functions of local composite operators from generalized unitarity
hep-th 2012-09 accept novelty 6.0 of 10

Generalized unitarity, previously used for scattering amplitudes, is extended to compute momentum-space correlation functions of local operators, yielding new n-point correlators of BPS and twist-2 operators in N=4 su...
Exact results for static and radiative fields of a quark in N=4 super Yang-Mills
hep-th 2012-02 conditional novelty 6.0 of 10

A D3-brane probe computation of the Lagrangian density one-point function around a static quark matches two prior results, motivating an exact all-N, all-coupling formula in terms of Laguerre polynomials.
Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
hep-th 2011-04 conditional novelty 6.0 of 10

In the Frolov-Tseytlin classical limit, weak-coupling coherent-state computations of three-point structure constants in planar N=4 SYM reproduce the strong-coupling string result, provided the heavy operators differ b...
Holographic three-point functions of giant gravitons
hep-th 2011-03 conditional novelty 6.0 of 10

The gauge-theory and semiclassical string-theory calculations of a two-giant-graviton plus one-pointlike-graviton three-point function disagree, and the authors attribute the mismatch to Schur polynomials failing to i...
Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
hep-th 2009-06 conditional novelty 6.0 of 10

Correlators of 1/8 BPS Wilson loops with chiral-primary local operators on a two-sphere are captured by a two-matrix model derived from two-dimensional Yang-Mills, and its planar strong-coupling limit matches the AdS5...

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125 later papers cite it

Evidence: substantial. 123 of the citing papers share no author with it, and 20 of those carry a confident label from Pith's citation classifier.

Pith read 20 of the 227 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 used its data or values and 1 compared its own results with it.

Uses its data or values 1 of 4 papers with this label

Used this paper's coupling constant λ_123 in its action for the scalar fields.

Matrix Model Maps and Reconstruction of AdS SUGRA Interactions (2007) · 0.97 · paraphrased: the licence does not allow quoting

Compares with it 1 of 11 papers with this label

Found canonically normalized three-point functions that agree with the results of this paper.

Large-N correlation functions in ${\cal N} = 2$ superconformal QCD (2016) · 1.00 · paraphrased: the licence does not allow quoting

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126 arXiv papers cite this in 231 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 · 156 sentences without a confident label

Builds on it 1 paper

From the gauge invariant scalar fields, one can define the same combinations as in ([ref]), now replacing the `bar' fields by the double `bar' ones, which satisfy the modified equations of motion [ref] : $- ℓ(ℓ-4)$ŝ̂^ℓ = 1/2(ℓ+2)$(ℓ+4)(ℓ+5)Q_1^ℓ+ Q_2^ℓ+ (ℓ+4)(D_μQ_3^μ^ℓ+ Q_4^ℓ)$, $- (ℓ+4)(ℓ+8)$t̂̂̂^ℓ = 1/2(ℓ+2)$ℓ(ℓ-1)Q_1^ℓ+ Q_2^ℓ- ℓ(D_μQ_3^μ^ℓ+ Q_4^ℓ)$, where the double `hat' notation is to emphasize that these are defined in terms of gauge invariant fields at quadratic order (i.e., they are built up from double `bar' fields).

Critical lumpy black holes in AdS${}_p\times S^q$ · Gauge invariance and equations at quadratic order · 0.82

Uses its method or tool 5 papers

The size of a BPS giant graviton is equal to its R-charge (angular momentum along $S^5$), which is related to its radial position in the AdS direction by [equation] To compute the three-point function we will need to compute the corrections to the D3-brane action coming from a light supergravity perturbation as in [ref] .

Orbit Averaging Coherent States: Holographic Three-Point Functions of AdS Giant Gravitons · AdS Giant Graviton Solution · 0.83
This entails expanding the equations of motion up to cubic order in fluctuations and performing field redefinitions to remove derivative couplings [ref] .

Precision holography of AdS$_5$ bubbling geometries · Discussion · 0.82
One way to calculate $⟨O^p_1 O^p_2 O^p_3 = p_1 + p_2⟩$ is by analytic continuation in $p_3$ [ref] .

How to Succeed at Holographic Correlators Without Really Trying · The traditional method · 0.92

Uses its data or values 4 papers

The normalization factor $c_Δ$ is the correct one obtained in [ref] .

Expectation values of chiral primary operators in holographic interface CFT · One-point function from gravity theory · 0.85
S = ∫d^5x √(-g) [ -∇s^I ∇s̅^I - m_I^2 |s^I|^2-λ_IJK (s^I s^J s̅^K+ c.c ) ] , where $m^2=j(j-4)$, and the coupling constant [ref] is λ_123 = (j_3-j_1-j_2) 2 κ√(j_1 j_2 j_3 (j_3^2-1)(j_3+2))(j_3-2)/√((j_1^2-1)(j_2^2-1)(j_1+2)(j_2+2)) ×f_123 , f_123 = 1/√(2π^3) √((j_1+1)(j_1+2) (j_2+1) (j_2+2))/√((j_3+1)(j_3+2)) .

Matrix Model Maps and Reconstruction of AdS SUGRA Interactions · Chiral Primary Interactions in $AdS_5 ×S^5$ · 0.97
It also determines the relative coefficient of $s_p_1-1$ and $s_p_1+1$ [equation] Note in our normalizations $λ_s_p$ is the product of three-point and one-point function coefficients $λ_s_p=C_p_1p_2pa_p$, with $C_p_1p_2p$ obtained in [ref] as $C_p_1p_2p=√(p_1p_2p)$.

Correlators of $\mathcal{N}=4$ SYM on real projective space at strong coupling · Introduction · 0.98

Compares with it 11 papers

We notice that the untwisted structure constants ([ref]) are actually $λ$-independent and, apart from the factor of $√(M)$ due to the $ℤ_M$ orbifold, they coincide with those of the $𝒩=4$ SYM theory [ref] .

Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories · Summary of results · 0.90
Further taking into account the rescaling ([ref]), the cubic coupling ([ref]) takes the form [equation] and this indeed is the result obtained in [ref] .

Cubic and higher-order supergravity couplings for AdS vacua using Exceptional Field Theory · Cubic scalar couplings · 1.00
We find <2k , 2k> = 2 k ( λ16 π)^2k , <2k_1 , 2k_2 , 2 k_1+2 k_2> = 8 k_1 k_2 (k_1+k_2) (λ16 π)^2 k_1+ 2k_2 If we normalize canonically the 2-point functions, we find <2k_1 , 2k_2 , 2 k_1+2 k_2> = 2√(2k_1 k_2 (k_1+k_2)) , which agrees with the results of [ref] .

Large-N correlation functions in ${\cal N} = 2$ superconformal QCD · Single trace 2- and 3-point functions at tree-level · 1.00

Cites it as support 1 paper

In agreement with non-renormalization theorems for protected operators [ref] , the quantum corrections are subleading in the dimensional regulator $ϵ$.

Tracing Transcendentality in Protected Correlators of N=4 SYM · Introduction · 0.96

Cites it as background 43 papers

Holographic three-point functions of giant gravitons have been studied extensively in the literature [ref] , with some discrepancies and ambiguities appearing between the holographic and gauge theoretic computations in the case of off-diagonal extremal correlators and for AdS giant gravitons.

Orbit Averaging Coherent States: Holographic Three-Point Functions of AdS Giant Gravitons · Introduction · 0.91
We start in section [ref] reviewing the $_5$ effective action, which is already known in the literature [ref] .

The Witten Diagram Bootstrap for Holographic Defects · Effective action at strong coupling · 0.93
We consider the case of $AdS_5 ×S^5$, which has been studied in [ref] .

Matrix Model Maps and Reconstruction of AdS SUGRA Interactions · Chiral Primary Interactions in $AdS_5 ×S^5$ · 0.94

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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