Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories

C. Sieg; J. A. Minahan; O. Ohlsson Sax

REVIEW

Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories

J. A. Minahan, O. Ohlsson Sax, C. Sieg

High Energy Physics - Theory · Submitted 17 Dec 2009 · 42 references

Pith's verdict: A careful, explicit four-loop computation whose wrapping result is genuinely cross-checked but whose headline h4(σ) has no independent published check.

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arXiv ID0912.3460 (version 2)

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CitationC. Sieg, J. A. Minahan, O. Ohlsson Sax. "Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories." arXiv:0912.3460 (2009). https://pith.science/paper/KHREZ3FC

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Bottom line: this is a careful, explicit four-loop computation whose wrapping result is genuinely cross-checked and whose headline number — h4(σ) = -(4+σ²)ζ(2) — is not, in print, independently checked. That asymmetry is the thing to know before you cite it. The stress-test note lands; I checked the specific claims and they hold up on reading the paper. The double-pole cancellation in appendix G constrains only the 1/ε² coefficients of Z4, which come from lower-loop subdivergences. h4 lives in the 1/ε coefficient of the {1} structure in (5.1), which that check never touches. The comparison with [27] covers only the maximal-shuffling terms {1,3},{3,1}, and those are fixed to -1 in (5.2) regardless of h4. And the GKV agreement in §6 is for the wrapping diagrams W1–W5, which are pure (λ̂λ)² and don't involve h4 at all. So the only direct check on h4 is [22], which is unpublished ('to appear') and shares an author. That's not nothing — the structural facts that the rational terms cancel and the result depends on couplings only through (λ+λ̂)⁴ are nontrivial consistency conditions — but it's not an independent verification. What's solid: the diagrammatics are laid out in full, every integral is tabulated, and the wrapping correction γ_w20 = (32-16ζ(2))λ̄⁴ matches the GKV Y-system prediction [23] from a different group. That's a real check on a real computation. The sign z=+1 is fixed by a genuine physical criterion (non-renormalization of the six-scalar vertex, appendix F), not fitted. The authors are also upfront that earlier versions had sign errors (footnote 3) and that the correction was triggered by the N=2 superspace work [22] — that transparency is worth something. The dimensional-reduction caveat in §4 is acknowledged by the authors and I'd treat it as a known open premise rather than a new finding; it's the standard assumption in this literature. Who should read it: anyone doing precision ABJM/ABJ integrability, or anyone who needs the four-loop dispersion coefficient as input. It's not a paper for outsiders. Recommendation: send it to referees. The computation deserves scrutiny, and the referee should be asked specifically to check the 1/ε coefficient of {1} in (5.1) — that's where the result actually lives.

Referee report

Major objections (3)

[§5, Eqs. (5.1)-(5.3), and §7] The central claim h4(σ) = -(4+σ²)ζ(2) rests on the 1/ε coefficient of the {1} structure in Z4 in Eq. (5.1), but the checks offered do not directly test this coefficient. The double-pole cancellation in appendix G constrains only the 1/ε² coefficients of Z4, which come from lower-loop subdivergences; the comparison with [27] in §5 covers only the maximal-shuffling terms {1,3} and {3,1}, which are fixed to -1 in Eq. (5.2) independently of h4; and the GKV agreement in §6 is specifically for the wrapping contribution γ_w20 = (32-16ζ(2))λ̄⁴, computed from diagrams W1-W5 that are pure (λ̂λ)² and do not involve h4. The only direct check on h4 is the unpublished, author-overlapping N=2 superspace computation [22]. Given the sign-error history disclosed in footnote 3, the authors should state explicitly which checks constrain which coefficients and, if possible, provide an additional independent verification of the 1/ε coefficient that determines h4.
[§4, p. 6] The validity of dimensional reduction at four loops is acknowledged as unchecked: the authors state that it 'has not explicitly been checked ... to four-loop order, but a breakdown appears very unlikely.' Since the pole parts of the individual diagrams determine h4, this is a load-bearing assumption for the central claim. The authors should discuss the evidence for dimensional reduction's validity at four loops more carefully, or estimate the potential impact of a breakdown on the pole parts and hence on h4.
[Appendix F, Eq. (F.2)] The sign z=+1 is fixed by requiring the six-scalar vertex not to renormalize, and this choice is load-bearing for the fermion-triangle diagrams (4.26)-(4.28) that contribute to the σ² term of h4. The authors should discuss the robustness of this choice and whether the h4 result is sensitive to it, especially given the sign discrepancy in the literature noted in footnote 7.

Minor objections (4)

[Appendix J] The parameter λ = 1/2 - ε in appendix J is distinct from the 't Hooft coupling λ used in the main text. This is noted in the appendix, but the reuse of the same symbol is potentially confusing; a different symbol would improve readability.
[§5] A summary table collecting the contributions to Z4 by diagram class (S, Sn, Fs, Ft) and their individual pole coefficients would help the reader follow the assembly of Eq. (5.1).
[References] Reference [22] is listed as 'to appear.' The authors should update this reference if it has since been published, since it is the only direct cross-check on h4.
[§2, Eq. (2.3)] The notation for the permutation structures {a1,...,am} could be clarified with an explicit example of how a product of permutations acts on the state (2.2), beyond the phase factors listed in Eq. (2.6).

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The paper

The paper claims

A brute-force four-loop Feynman calculation in the ABJM/ABJ Chern-Simons theories fixes the magnon dispersion function to $h^2(λ̄,σ)=λ̄^2-(4+σ^2)ζ(2)λ̄^4$ and reproduces the Y-system's prediction for the four-loop wrapping correction to a长度

The reading

This paper is the detailed companion to an earlier letter. It sets out, diagram by diagram and integral by integral, the four-loop perturbative calculation that pins down the unknown coupling-dependent function $h^2(λ̄,σ)$ appearing in the magnon dispersion relation of the spin chains dual to $N=6$ superconformal Chern-Simons matter theories (the ABJM model and its $U(M)×U(N)$ ABJ generalisation). Working in the $SU(2)×SU(2)$ flavour sector, the authors renormalize single-trace operators, extract the four-loop dilatation operator from the pole parts of the graphs, and read off $h_4(σ)=-(4+σ^2)ζ(2)$. They then compute the four-loop wrapping correction for the length-four operator in the $20$ of $SU(4)$ and obtain $γ^{20}_w=(32-16ζ(2))λ̄^4$, which matches the prediction of the proposed $Y$-system. The stake is that both the dispersion relation and the wrapping correction are outputs of integrability that had never been confronted with direct field theory at this order; the paper's answer is that they survive the confrontation.

What carries the argument

The load-bearing device is the dilatation operator written as an expansion in permutation structures $P_{2i+a_1 2i+a_1+2}P_{2i+a_2 2i+a_2+2}…$ summed along the chain, so that $D_4$ is a short linear combination of $D_4=(h_4-4){} +(6-h_4){1} -{1,3}-{3,1}$ acting on odd sites (and the $σ→-σ$ image on even sites). Acting with these structures on a single-magnon momentum eigenstate produces phase factors $e^{±ip}$, and matching against the expansion of $E(p)=√(Q^2+4h^2(λ̄,σ)sin^2(p/2))-Q$ converts a Feynman calculation into a single number $h_4$. The Feynman calculation itself runs through the renormalization constant $Z=1+λ̄^2Z_2+λ̄^4Z_4+…$, with $D=μ d/dμ ln Z$; the logarithm is what guarantees that double poles cancel, and appendix G exhibits that cancellation explicitly as a check. Dimensional reduction is used throughout: tensor algebra in exactly three dimensions, then the integrals continued to $D=3-2ε$ and evaluated with scalar $G$-functions and the triangle reduction rules collected in the appendices.

Extended reading notes

Core claim

The central claim is that the four-loop term of the magnon dispersion function is $h_4(σ)=-(4+σ^2)ζ(2)$, i.e. $h^2(λ̄,σ)=λ̄^2-(4+σ^2)ζ(2)λ̄^4$, so that to four loops the function is even in $σ=λ-λ̂$ and there is no parity-breaking split between the dispersion relations of magnons on odd and even spin-chain sites. The rational parts cancel, leaving a maximally transcendental coefficient, and once $σ$ is written out the four-loop term depends on the two 't Hooft couplings only through $(λ+λ̂)^4$. The companion claim is that the four-loop wrapping correction to the anomalous dimension of the length-four operator in the $20$ of $SU(4)$ is $γ^{20}_w=(32-16ζ(2))λ̄^4$, in agreement with the $Y$-system prediction, and that the full four-loop anomalous dimension of that operator is $γ^{20}=4+8λ̄^2-8(6+σ^2)ζ(2)λ̄^4$, again with the rational terms cancelling. The paper also records that earlier versions of this work contained sign errors traceable to inconsistent Feynman rules, and that the corrected propagators and scalar-gauge vertices given in the appendix, together with the sign $z=+1$ fixed by requiring the six-scalar vertex not to renormalize at two loops, are what the present numbers rest on.

Load-bearing premise

The whole calculation assumes that dimensional reduction — doing the tensor algebra in exactly three dimensions and then continuing the integrals to $D=3-2ε$ — preserves gauge invariance and the Slavnov-Taylor identities at four loops, something the authors state has not been checked at that order and which they judge unlikely to fail.

Editorial extensions

If this is right

The all-loop Bethe ansatz for ABJM/ABJ can be trusted at four loops in the $SU(2)×SU(2)$ sector: the dispersion function entering it is now known to order $λ̄^4$, with no parity-odd term.
The $Y$-system proposal for the ABJM model survives its first direct wrapping test, since the four-loop wrapping correction computed from explicit diagrams coincides with its prediction.
Because $h_4=-4ζ(2)$ is negative, the small-$λ̄$ quadratic behaviour of $h^2$ is damped toward the linear large-coupling behaviour inferred from the IIA string BMN limit.
The four-loop wrapping correction is independent of $σ$, consistent with the topology of the wrapping diagrams and with the two-loop result also being $σ$-independent.
The full four-loop anomalous dimension of the length-four $20$ operator contains only terms of maximum transcendentality, since the rational pieces of the asymptotic and wrapping contributions cancel.

Reading between the lines

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

If the $Y$-system and the direct perturbative route agree at four loops in this sector, the natural next test is the six-loop order, where magnons on odd and even sites begin to interact and where a parity-odd piece of $h^2$ could first appear.
The reported $σ$-independence of the wrapping correction suggests that wrapping diagrams in this sector are blind to the $U(M)×U(N)$ asymmetry, which would be a useful structural hint for anyone trying to extend the TBA to the ABJ case.
The history noted in the paper — a sign error caught only by disagreement with an independent superspace computation — argues that the most efficient check on results of this kind is a second formalism rather than more diagrams within the same one.
Since the four-loop term depends on the couplings only through $(λ+λ̂)^4$, one might look for a scheme or a variable in which the dispersion function's expansion truncates or reorganises along that combination.

Original abstract

In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the logarithm of the renormalization constant.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.33 · mentions code or data availability 0.04.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the logarithm of the renormalization constant.

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	In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories.	background 0.90	0.76	0.12	asserted 1.00
s1	In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories.	contribution 1.00	0.93	0.19	asserted 0.99
s2	Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the logarithm of the renormalization constant.	contribution 0.83	0.94	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.70.

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arXiv listing abstract v2

not examined

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References

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Forward citations

Cited by 8 Pith papers

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The tricritical Ising CFT and conformal bootstrap
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First conformal-bootstrap islands for the tricritical Ising CFT in d=2.5 and d=2.75, consistent with Padé interpolations between the 3−ε expansion and the exact 2d minimal model.
Exact Bremsstrahlung functions in ABJM theory
hep-th 2018-02 conditional novelty 7.0 of 10

A defect supersymmetric Ward identity proves B^phi_{1/6} = 2 B^theta_{1/6} in ABJM theory, and localization yields an exact elliptic-integral closed form for B_{1/2}.
Non-conformality of gamma_i-deformed N=4 SYM theory
hep-th 2013-08 conditional novelty 7.0 of 10

The gamma_i-deformed N=4 SYM theory is not conformally invariant: a double-trace coupling has a one-loop beta function that is a sum of squares and cannot be cancelled by any allowed multi-trace extension.
Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
hep-th 2016-12 accept novelty 6.0 of 10

Taking a combined weak-coupling, large-imaginary-twist limit of gamma-deformed N=4 SYM and ABJM yields chiral non-gauge theories with doubly-scaled Bethe equations that constrain five-loop Feynman integrals.
Wronskian Solution for AdS/CFT Y-system
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The full quantum Y-system of planar AdS5/CFT4 is solved in closed form as Wronskian determinants of eight Baxter Q-functions, with explicit large-size asymptotic expressions.

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Roadmap on Wilson loops in 3d Chern-Simons-matter theories
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The review organizes the state of the art on ABJ(M) Wilson loops and introduces a manifestly reparametrization-invariant superconnection formulation of the 1/6 BPS fermionic loop.
Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
hep-th 2017-06 conditional novelty 5.0 of 10

The Bremsstrahlung function of the 1/2 BPS cusp in ABJM theory equals one over four pi squared times the derivative of the deformed circular Wilson loop with respect to the deformation parameter, derived from defect t...
Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
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The chapter consolidates how planar ABJM theory and IIA strings on AdS4xCP3 both reduce to an alternating OSp(6|4) spin chain, and catalogues where the Bethe equations, S-matrix and algebraic curve differ from the AdS5 case.

How later papers used it

45 later papers cite it

Evidence: substantial. 37 of the citing papers share no author with it, and 13 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 109 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

4 later papers by other authors are listed below: 2 used its method or tool and 2 used its data or values.

Uses its method or tool 2 of 4 papers with this label

Used the effective rule of eq. (A.7) of this paper, along with the FIRE package, to find its result.

Form Factors of Chiral Primary Operators at Two Loops in ABJ(M) (2013) · 0.94 · paraphrased: the licence does not allow quoting
Used the machinery developed in this paper and employed in a very similar setting, the calculation of the two-loop form factor of CPO's, in another work.

ABJ(M) Chiral Primary Three-Point Function at Two-loops (2014) · 0.99 · paraphrased: the licence does not allow quoting

Uses its data or values 2 of 6 papers with this label

Used the value of the ABJM scaling function at four loops from this paper in its expansion of the ansatz.

An all order identity between ABJM and N=4 SYM four-point amplitudes (2011) · 0.93 · paraphrased: the licence does not allow quoting
Used the expression for the 2-loop correction to the scalar propagator given for instance in this paper to compute diagram (p_1).

ABJM $\theta$-Bremsstrahlung at four loops and beyond (2017) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

45 arXiv papers cite this in 109 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 · 69 sentences without a confident label

Contests it 1 paper

We find that the effective rule given in [ref] for $I_4$ gives inconsistent results in our case.

Form Factors of Chiral Primary Operators at Two Loops in ABJ(M) · Effective rule for $I_4$ · contest 0.89

Uses its method or tool 4 papers

We use the machinery developed in [ref] and employed in a very similar setting, the calculation of the two-loop form factor of CPO's, in [ref] .

ABJ(M) Chiral Primary Three-Point Function at Two-loops · Calculational details · 0.99
These diagrams are evaluated using the Feynman rules published in [ref] (note that these Feynman rules capture only the planar contributions which is sufficient for the present calculation) and used already in [ref] .

An Extremal Chiral Primary Three-Point Function at Two-loops in ABJ(M) · Feynman diagrammatics · 1.00
With the exception of [ref](h) (which will be discussed in more detail shortly), the momentum integrals obtained after performing the superspace $D$-algebra in these diagrams may be expressed using integration by parts in terms of a relatively small basis of momentum integrals [ref] which are depicted in Table [ref], and whose divergences are also listed in Appendix B.

The a-function for N=2 supersymmetric gauge theories in three dimensions · Four-loop calculation · 0.92

Uses its data or values 6 papers

Since at weak coupling $h(λ)$ is known up to the forth order [ref] , we easily find f_CS(λ)= 4 λ^2 - 24 ζ_2 λ^4 + O(λ^6) and the ansatz ([ref]) provides a prediction for the four–loop expression of the finite remainder $F_4^(4)$ (in the notation of [ref] ) for the ABJM four–point scattering amplitude [ref]

Scattering in ABJ theories · BDS–like ansatz · 0.85
And (on the string side) $Δ$ is the energy, $J$ and $Q$ are $CP^3$ angular momenta, and $S$ is an $AdS_4$ angular momentum. ] [equation] Four-loop gauge theory calculations [ref] show that $h_4=-4ζ(2)≈-6.58$.

Quantum Strings and the AdS4/CFT3 Interpolating Function · Introduction · 0.98
M_3d^(4)(,μ_A) = 1/2 [ f_CS^(2)() ( M_4d^(1)(2,μ”) + D() ) + C_CS^(2)() ]^2 + f_CS^(4)() ( M_4d^(1)(4,μ”) + D(2) + C_CS^(4)() ) obtained from the expansion of the ansatz ([ref]), and the value of the ABJM scaling function at four–loops [ref] f_CS(λ)= 4 λ^2 - 24 ζ_2 λ^4 + O(λ^6) which leads to

An all order identity between ABJM and N=4 SYM four-point amplitudes · A conjecture for the four–loop amplitude · 0.93

Compares with it 8 papers

It reads [equation] Now, by subtracting from [ref] the range five contribution and inserting $h_4(σ)=-(4+σ^2)ζ(2)$, the subtracted dilatation operator becomes [equation] The dilatation operator for length four states then reads [equation] and it coincides with the results obtained in terms of component fields [ref] .

Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories · Wrapping interactions · 0.99
This expansion can be compared against the direct 4-loop perturbative calculation of [ref] (later also confirmed in [ref] ), which gives h_4-loop^2(λ_1,λ_2)=λ_1λ_2+h_4$λ_1λ_2$^2+h_4,σλ_1λ_2(λ_1-λ_2)^2 where h_4=-2π^2/3, h_4,σ=-π^2/6 , perfectly matching our result!

On the Exact Interpolating Function in ABJ Theory · Weak coupling limit · 1.00
As expected, at weak coupling our numerical results are completely consistent with the leading wrapping correction obtained analytically in [ref] , [ref] (this is also seen in Figure [ref]).

Numerical results for the exact spectrum of planar AdS4/CFT3 · Numerical results · 0.99

Cites it as support 1 paper

Indeed, it was explicitly shown in [ref] and [ref] by direct computations, that this is true at four-loop order: the contributions to the dilatation operator of the diagrams that could lead to interactions between the two types of magnons cancel.

The Leading Order Dressing Phase in ABJM Theory · Introduction · 0.98

Cites it as background 5 papers

Analogous checks have been done for AdS$_4$/CFT$_3$ – the four-loop wrapping corrections obtained in [ref] were reproduced in [ref] , [ref] , while in [ref] the proposed Y-system and TBA were shown to be remarkably consistent with the algebraic curve quantization [ref] .

Numerical results for the exact spectrum of planar AdS4/CFT3 · Introduction · 0.86
In turn, this knowledge of $Γ_cusp$ could give insight on the non-perturbative structure of the interpolating function $h(λ)$ of ABJM [ref] , which percolates in every integrability-based computation made in this three-dimensional theory.

Higher-loop integrated negative geometries in ABJM · Introduction · 0.88
Having this new $_4/_3$ duality naturally brings up the question of its integrability which in fact has received a lot of attention [ref] , [ref] .

Finite-size corrections for quantum strings on AdS_4 x CP^3 · Introduction and summary · 0.96

What it cites · 27 sentences without a confident label

Contests 2 papers

The two-loop renormalization of the six-scalar vertex allows us to fix a sign discrepancy in the literature[The antisymmetric parts in the product of two $γ$ matrices [ref] in [ref] and [ref] differ by a sign.] parameterized by $z=±1$ which affects the four-loop diagrams with fermion triangles, c.f.

Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence · Two-loop renormalization of the six-scalar vertex · contest 0.74
The two-loop renormalization of the six-scalar vertex allows us to fix a sign discrepancy in the literature[The antisymmetric parts in the product of two $γ$ matrices [ref] in [ref] and [ref] differ by a sign.] parameterized by $z=±1$ which affects the four-loop diagrams with fermion triangles, c.f.

Integrable Spin Chain in Superconformal Chern-Simons Theory · Two-loop renormalization of the six-scalar vertex · contest 0.74

Uses the method or tool of 2 papers

[equation] The above final four-loop integrals have also been checked by using the Gegenbauer polynomial $x$-space technique (GPXT) as formulated in [ref] and extended in [ref] .

Anomalous dimension with wrapping at four loops in N=4 SYM · Four-loop integrals with central quartic vertex · 0.99
Following the strategy of [ref] , we first subtract from the asymptotic dilatation operator [ref] the range five interactions (given by $S_2$ and the reflected diagram).

Wrapping at four loops in N=4 SYM · Four-loop wrapping interactions · 0.97

Compares with 7 papers

Hence the four-loop wrapping contribution to the anomalous dimension is [equation] which agrees with the GKV $Y$-system prediction [ref] .

Integrability for the Full Spectrum of Planar AdS/CFT · Four-loop wrapping interactions · 0.99
Our result matches prediction of Gromov, Kazakov and Vieira [ref] which they obtained by means of the proposed $Y$-system [ref] for the ABJM model.

Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model · Introduction and summary of results · 1.00
Our result matches prediction of Gromov, Kazakov and Vieira [ref] which they obtained by means of the proposed $Y$-system [ref] for the ABJM model.

Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal · Introduction and summary of results · 1.00

Cites as background 3 papers

To the best of our knowledge, integrability makes no prediction for $h^2(λ)$, but there exist some alternative analyses not based on integrability [ref] .

Three-dimensional N=6 SCFT's and their membrane dynamics · Introduction and summary of results · 0.85
To the best of our knowledge, integrability makes no prediction for $h^2(λ)$, but there exist some alternative analyses not based on integrability [ref] .

S-duality and the giant magnon dispersion relation · Introduction and summary of results · 0.85
The gravity dual for the ABJM model is $M$-theory on $AdS_4×S^7/Z_k$ [ref] , where the compact space $S^7/Z_k$ is equivalent to $CP^3$ with a $U(1)$ fibration.

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction and summary of results · 0.98

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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