Universal holographic Wilson loops in 3d SCFTs

Alexia Nix; Fridrik Freyr Gautason

REVIEW 2 major objections 5 minor 1 cited by

Universal holographic Wilson loops in 3d SCFTs

T0 review · 2 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper derives universal one-loop predictions for the vacuum expectation values of half-BPS Wilson loops in two large families of three-dimensional superconformal Chern-Simons-matter theories, using only the geometry of their holographi

desk verdict Universal one-loop M2 and string Wilson-loop calculation that checks out for ABJM/ADHM and makes new predictions; the family B prefactor is plausible but rests on a regularization scheme that still needs an independent anchor. read the letter →

arxiv 2511.04596 v2 pith:KSZUKQJI submitted 2025-11-06 hep-th

Fridrik Freyr Gautason , Alexia Nix This is my paper · ORCID

classification hep-th PACS 11.25.Tq04.65.+e

keywords AdS4/CFT3WilsonloopsM2-braneone-loopquantizationSasaki-EinsteingeometryChern-Simons-mattertheoriesmassivetypeIIAAiryfunction

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The authors establish a universal one-loop expression for the vacuum expectation value of half-BPS Wilson loops in two large families of N=2 Chern-Simons-matter SCFTs. For theories with M-theory duals (family A), the M2-brane partition function at one loop depends only on the radius c of the M-theory circle and three charges q_l read off from the SE7 metric; for theories with massive type IIA duals (family B), the string one-loop partition function depends only on N, the sum n of Chern-Simons levels, and the volume of the SE5 base. Combining the one-loop prefactor with a conjectured Airy completion yields a closed-form, perturbatively exact prediction for family A. The authors test against known ABJM, ADHM and Q^{1,1,1} results and provide new predictions for V^{5,2} and M^{3,2} and for all family B models.

What carries the argument

The engine of the computation is the quadratic fluctuation action around the classical brane: an M2-brane wrapping a calibrated circle S^1_M inside SE7, or a fundamental string at α=0 in the sine-cone geometry. Using Sasaki-Einstein geometry — specifically the relation R_{0a0b}=δ_ab for the curvature along the Reeb direction and the vanishing of extrinsic curvature — the fluctuation spectrum reduces to massive Klein-Gordon and Dirac operators on AdS2, with masses set by c and the charges q_l (eigenvalues of the spin connection pullback). The same spectrum is obtained for the string after the mass matrix is shown to be universal. The one-loop determinants are evaluated with heat-kernel/zeta r

What would settle it

Carry out the next-to-leading-order matrix-model computation of the 1/2-BPS Wilson loop for a family B gauge theory (e.g., SU(N)_k Chern-Simons-matter with a single level) and compare the coefficient of N^{1/3} in the exponent and the prefactor with (5.25). Any discrepancy in the prefactor would falsify the universal one-loop string determinant; for family A, a numerical evaluation of the Airy ratio (3.31) for V^{5,2}/Z_{N_f} against the matrix model would test the one-loop exactness and ensemble conjecture.

Watch

Extended reading notes

Core claim

At the paper's core is a universal statement about the semiclassical quantization of the holographic duals of 1/2-BPS Wilson loops in three-dimensional superconformal Chern-Simons-matter theories. For family A — the theories with AdS4 x SE7 M-theory duals — the one-loop M2-brane effective action is a function only of c, the radius of the M-theory circle, and three charges q_l; the authors conjecture that after a Laplace transform from the grand canonical to the canonical ensemble, the full perturbative Wilson loop is the ratio of Airy functions (3.31). For family B — the massive type IIA duals on warped AdS4 x S(SE5) — the one-loop string determinant is independent of the detailed Sasaki-Ein

Load-bearing premise

The M2-brane partition function is assumed to be one-loop exact and to compute the Wilson loop in the grand canonical (fixed chemical potential) ensemble; if this fails, the Airy ratio (3.31) is not the correct all-orders completion, though the one-loop prefactor would survive.

Editorial extensions

If this is right

For every SCFT in family A with a known SE7 dual, the one-loop M2-brane partition function is given by (3.23)-(3.25), and the perturbatively exact Wilson loop VEV is the Airy ratio (3.31), with no free parameters.
The ABJM, ADHM and Q^{1,1,1}/Z_{N_f} results reproduce known matrix-model answers, confirming the universality of the one-loop prefactor.
For family B, the Wilson loop VEV at next-to-leading order is (5.25), scaling as N^{1/3} exp(...), with prefactor fixed by Γ(2/3)^3 and the SE5 volume; this is a new prediction to be tested by matrix models.
The string-theory expansion coefficients a_p in (3.36) can be extracted from Γ_M2; for ABJM, ADHM and Q^{1,1,1} they take a universal trigonometric form, while V^{5,2} is more involved.
The results imply that the leading exponential is fixed by geometry and the prefactor by one-loop determinants, so no per-theory fitting is needed.

Reading between the lines

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

Inference: If the one-loop exactness/ensemble assumption holds for family A, the same method could be applied to other M2-brane observables, such as worldsheet instanton prefactors, giving a general framework for precision holography in AdS4.
Inference: The universal string spectrum for family B suggests a similar universality for the four-dimensional parent theories, where the a-central charge and volumes appear; the 3d result might be obtainable from a topological string or free-energy extremization in the parent.
Inference: The dependence of the M2 result only on c and q_l hints that these quantities may map to simple field-theoretic data (R-charges/levels), allowing the Airy B parameter to be fixed without a full matrix-model computation in cases like V^{5,2}/Z_k and M^{3,2}/Z_k.
Inference: A testable extension is to compute the O(e^{-#√N}) non-perturbative corrections to (3.31) by including membrane instantons and compare with the known ABJM instanton series; this would test whether the Laplace-transform completion captures the full trans-series.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

I think this is a genuinely useful paper, and the main result is real. The authors show that the one-loop partition function of the M2-brane dual to the Wilson loop in AdS4×SE7 depends only on the M-theory circle radius c and three charges q_l, and they compute it for arbitrary SE7. They also do the first one-loop string calculation for the massive IIA family B. The ABJM and ADHM checks reproduce known answers, which gives confidence that the machinery is right. The new examples (Q111, V5,2, M3,2) are predictions, not checks.

The family A Airy ratio (3.31) is a conjecture, and the authors say so. It relies on the grand-canonical one-loop-exactness assumption from [14]. That's a real soft spot, but it's clearly flagged and doesn't affect the one-loop prefactor itself.

The bigger soft spot is family B. The mass spectrum is derived cleanly and is universal, but the finite part of the one-loop determinant (5.24) requires replacing a UV cutoff log Λ by log(ℓ/2πℓ_s), citing [36]. That is a scheme choice. It worked for AdS4×CP3 where localization could check it, but for massive IIA there is no independent matrix-model result. If the correct scheme differs by a constant, the prefactor changes by an O(1) factor; if it differs in the log of the AdS scale, the N-scaling changes. The stress-test note claims the latter is possible, and I think that's a fair concern. The authors note the lack of a field-theory anchor themselves, so I don't see it as an error, just an unvalidated assumption in the only genuinely new numerical prediction.

What the paper does well: the universal spectra are carefully derived, the heat-kernel sums are explicit, and the reduction to type IIA is sensible. The writing is clear and honest about what is conjecture and what is computation.

Who should read it: anyone doing precision holography in AdS4/CFT3, or working on quantum string/M2 partition functions. I would send it to a serious referee. The referee should focus on Section 5.1 and the Airy step, not on the overall method.

My own bottom line: the one-loop computations are probably correct; the family B prefactor is a plausible prediction but not yet a tested one. It deserves to be published after the usual scrutiny.

Referee Report

2 major / 5 minor

Summary. The paper studies the large-N vacuum expectation value of 1/2-BPS Wilson loops in two families of three-dimensional N=2 Chern-Simons-matter theories. For family A, dual to AdS4 x SE7 in M-theory, the authors compute the one-loop partition function of a probe M2-brane wrapping AdS2 x S^1_M and obtain a universal prefactor depending on the M-theory-circle radius c and three charges q_l, Eqs. (3.23)-(3.26). They then conjecture a full perturbative completion as a ratio of Airy functions, Eq. (3.31), following the ensemble proposal of [14]. For family B, dual to massive type IIA backgrounds AdS4 x S(SE5), they compute the one-loop partition function of a fundamental string, Eq. (5.24), and obtain a universal Wilson-loop prediction, Eq. (5.25), depending only on N, n, and vol(SE5). The ABJM and ADHM examples reproduce known matrix-model results, and several further examples are worked out.

Significance. If the one-loop results are correct, the paper provides genuinely universal, parameter-free prefactors for Wilson loops in a broad class of holographic SCFTs. The ABJM and ADHM comparisons are strong external checks and demonstrate that the heat-kernel and determinant-sum machinery is implemented correctly. The family-B result, Eq. (5.25), is the first subleading prediction for that class and is falsifiable once matrix-model techniques reach this order. The Airy completion (3.31) is clearly labeled as speculative, but it is the basis for the advertised full perturbative completion. The paper is careful about geometric data and openly acknowledges missing B parameters and the absence of a field-theory check for family B; these strengths and caveats are appropriately balanced. The main unresolved issues are the scheme-dependence of the family-B cutoff replacement and the reliance on the ensemble/one-loop-exactness assumption from [14] for the all-orders formula.

major comments (2)

[Section 5.1, Eqs. (5.23)-(5.25)] The finite part of the F1 one-loop determinant, and therefore the prefactor in (5.25), is obtained by replacing the UV cutoff Λ with ℓ/(2πℓ_s) after (5.23), following [36]. In the ABJM/CP3 context this replacement was validated against localization, but for the massive IIA backgrounds there is no independent matrix-model anchor. The logarithmic divergence is universal (b2,tot=R^(2), χ=1, Appendix B), but the finite part is scheme-dependent. Since ℓ/ℓ_s behaves as a positive power of N/n, a different scheme — e.g. log Λ ~ log(1/ℓ_s) or an added O(1) constant — would change the prefactor in (5.25) by a power of N or by an O(1) factor, altering the N-scaling of the prediction. The V5,2 zero-mode comparison fixes the mass spectrum, not the path-integral measure. This is load-bearing for the paper's main new family-B claim and should be stated as an assumption or supported by an independent c
[Section 3.3, Eqs. (3.29)-(3.31)] The passage from the one-loop M2-brane result (3.26) to the all-orders Airy ratio (3.31) assumes both one-loop exactness of the M2-brane partition function and a grand-canonical-to-canonical Laplace transform, following [14]. The text explicitly calls this speculative, but (3.31) is then used for the advertised full perturbative completion and for several family-A examples. Since [14] is a recent companion proposal and the ABJM/ADHM checks were already obtainable by other methods, the all-orders formula is not yet independently tested. I recommend separating the one-loop prediction, which is on firmer ground, from the Airy completion, and stating clearly that the latter is contingent on the ensemble/exactness proposal.

minor comments (5)

[Section 4.1, Eq. (4.15)] The match with [15] is quoted 'up to a factor of 1/2 due to a different normalization convention.' Please specify the exact normalization convention so that future comparisons do not inherit an ambiguity.
[Table 1 and Sections 4.3.2, 4.4.2, 4.5] Several entries have unknown B parameters, so formulas such as (4.48) and (4.57) contain an undetermined shift. This is acknowledged, but it would help to mark these explicitly as predictions up to B rather than complete closed forms.
[Section 5.1, Eqs. (5.26)-(5.32)] The notation λ for family A and \tilde λ for family B is easy to confuse; define them side by side. The scaling argument from (5.27) to (5.31) is heuristic and should not be presented as a check of the O(1) coefficient in (5.25).
[Section 4.3.2, Eq. (4.34)] The result e^{-Γ_M2}=2k is surprising because it suggests the k≫1 string-theory limit is exact. A short comment on the physical interpretation, or a check of the next correction, would strengthen this example.
[Abstract and Section 3.3] The abstract says 'we conjecture the full perturbative completion', while the text says 'we speculate'; aligning the wording and summarizing the two assumptions behind the Airy formula would improve clarity.

Circularity Check

1 steps flagged · score 2.0 of 10

No construction-level circularity; the one-loop determinants are derived from the background geometry and heat-kernel data, with ABJM/ADHM as external checks. The only mild self-citation burden is the grand-canonical/one-loop-exact completion for family A, which is taken from the authors' own [14] and explicitly flagged as a conjecture.

self citation load bearing [Section 3.3, eqs. (3.29)-(3.31); also Introduction and Conclusions]
"However recently [14], it has been argued that the M2-brane partition function does not compute the Wilson loop vacuum expectation value in the canonical ensemble in the dual field theory. ... In [14] it was noticed that for many examples, the M2-brane partition function is one-loop exact ... We will however speculate that the M2-brane partition function discussed above is one-loop exact and thus we may use the Laplace transform above to give a formula that is perturbatively exact in N for the Wilson loop in the canonical ensemble."

The Airy-ratio completion (3.31) is obtained by combining the classical shift e^{2cμ} with the assumption that the M2-brane grand-canonical partition function is one-loop exact. The cited justification is [14], a paper by the present first author; the assumption is not re-derived in this paper and, where no independent Airy or matrix-model check is available, (3.31) rests on that self-citation. This is an evidential burden, but not a construction-level circularity: the one-loop prefactor e^{-Γ_M2} is computed from the geometry and heat-kernel determinants, and it is externally matched for ABJM and ADHM; the text also explicitly labels the completion as a conjecture.

full rationale

The central one-loop derivations are self-contained rather than circular. For family A, the M2-brane fluctuation spectrum is obtained from the universal quadratic action (3.13), with charges q_l fixed by the SE7 spin connection and c fixed by the calibrated M-theory circle; no Wilson-loop answer is used as input. For family B, the string one-loop determinant follows from the universal mass matrices derived in Appendix C and the heat-kernel determinants, again without fitting to the predicted vev. External anchors exist where the prediction can be tested: the ABJM prefactor (4.15) matches [15] up to an explained normalization, the ADHM result (4.24) matches [37], and the leading exponential behaviour matches earlier matrix-model results [4,13]. The family-B prefactor (5.24)-(5.25) does involve the scheme-dependent replacement logΛ→log(ℓ/(2πℓ_s)) inherited from [36]; this is a regularization choice and thus a correctness caveat rather than circularity, especially since the text itself admits 'with no field theory answer to compare to, one might propose that there is no evidence in support of the above prediction' (Section 5.1). The only self-citation concern is [14], which supplies the grand-canonical/one-loop-exact framework for the Airy ratio (3.31); this is explicitly speculative and does not affect the independent one-loop prefactor. Accordingly, the circularity score is low: 2.

Assumptions & free parameters 3 free parameters · 8 assumptions · 0 invented entities

The central claim is largely self-contained once the standard holographic dictionary and heat-kernel technology are accepted. The main external inputs are the classical M2 configuration from [13], the grand-canonical one-loop exactness proposal from [14], and known Airy parameters from matrix-model literature; no Wilson-loop data are fitted. For family B, the log-divergence regularization prescription of [36] is an additional scheme assumption.

free parameters (3)

M-theory circle radius c (per example) = ABJM: 1/k; ADHM: 1/N_f; Q111/ZNf: 1/(2N_f); Q111/Zk: 1/(4k); V5,2/ZNf: 3/(4N_f); V5,2/Zk: 3/(4k); M3,2/Zk: 3/(8k)
Central input to (3.23-3.26) and (3.31). Computed from each explicit SE7 metric and the chosen M-theory circle, not fitted to Wilson-loop data; included for transparency.
Charges q_l (per example) = ABJM/Q111/ZNf: {3,1,-1,-1}; ADHM: {3,-1,0,0}; Q111/Zk: {3,1,1,-3}; V5,2: {3,-1/3,-1/3,-1/3}; M3,2/Zk: {3,-5/3,-1/3,1}
Eigenvalues of the spin-connection along the M-theory circle; determine the spectrum in Table 2. Derived from geometry, not fitted.
Airy shift parameter B = varies by theory; unknown for Q111/Zk, V5,2/Zk, M3,2/Zk
Taken from matrix-model literature (Table 1); needed for (3.31)/(4.48)/(4.57). Where unknown, the prediction is incomplete as a function of B, not a numerical prediction.

assumptions (8)

domain assumption The holographic dictionary ⟨W⟩ = Z_probe brane ≈ e^{-S_cl} Z_1-loop (with higher-loop and nonperturbative corrections neglected)
Used throughout Sections 3 and 5; standard in precision holography but not derived from field theory.
domain assumption The backgrounds AdS4×SE7 (family A) and warped AdS4×S(SE5) massive IIA (family B) are the correct holographic duals of the SCFTs considered
Assumed from prior AdS4/CFT3 literature; invoked in Sections 2-5.
domain assumption For family B, all Chern-Simons levels are equal, k_i = k, so n = Gk
Stated in Section 2 as an additional assumption following [4]; needed for (1.1)/(5.25).
domain assumption The classical M2-brane wraps an M-theory circle at critical points of h_M where ζ_M ∝ ζ_R, with the configuration of [13]
Used in Section 3.1 to set the classical action and normal-bundle decomposition.
ad hoc to paper The M2-brane partition function is one-loop exact and computes the grand canonical ensemble; canonical ensemble is obtained by Laplace transform (from [14])
Speculative premise required for the Airy completion (3.31); the text says 'we speculate' in Section 3.3.
domain assumption The Airy conjecture for the sphere partition function, Z_p = C^{-1/3} e^A Ai(C^{-1/3}(N-B))
Taken from [22]; used to convert the grand-canonical Laplace transform into (3.31).
domain assumption String one-loop log divergence is regularized by replacing log Λ with log(ℓ/(2πℓ_s)) and using the Euler-characteristic counterterm (method of [36])
Needed for family B result (5.23)-(5.24); a change of scheme could shift the prefactor.
standard math Sasaki-Einstein identities: R0a0b = δ_ab and Σ q_l = -1, plus standard heat-kernel zeta-function determinant formulas
Derived/collected in Appendices A and B; support the universal spectrum and determinant evaluation.

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Pith. "Pith review of Universal holographic Wilson loops in 3d SCFTs." pith.science (2026). https://pith.science/paper/KSZUKQJI

@misc{pith2026251104596,
  author       = {Pith},
  title        = {Pith review of: Universal holographic Wilson loops in 3d SCFTs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KSZUKQJI}},
  note         = {Machine review of arXiv:2511.04596}
}

abstract

We study the vacuum expectation value of half-BPS Wilson loop operators in two families of superconformal $\mathcal{N}=2$ Chern-Simons-matter theories. The first family is dual to AdS$_{4}$ solutions in M-theory, while the second one has a dual description in massive type IIA string theory. Utilizing the properties of the underlying geometry, we provide a universal description for the semiclassical quantization of a probe M2-brane and fundamental string in the respective holographic dual geometries. As a result, we find the one-loop partition function of both the M2-brane and the string which leads to a prediction for the large $N$ behaviour of the Wilson loops in the dual SCFTs. For theories with M-theory duals, we conjecture the full perturbative completion as a ratio of Airy functions.

Figures

Figures reproduced from arXiv: 2511.04596 by the authors.

**Figure 2.** Quiver diagram of ABJM. Now, the metric of the eleven-dimensional dual geometry is given by (3.1) with the S 7/Zk metric given by ds 2 S7 = ds 2 CP3 + η 2 , (4.2) where the Kähler-Einstein metric reads ds 2 CP3 = X 6 i=1 (e i ) 2 , (4.3) with frames e i given by e 1 = dθ , e2 = 1 2 sin θdθ1 , e3 = 1 2 sin θ sin θ1dϕ1 , e 4 = 1 2 cos θdθ2 , e5 = 1 2 cos θ sin θ2dϕ2 , e 6 = 1 2 sin θ cos θ(2 dφ + cos θ1dϕ1 − cos θ2dϕ2… view at source ↗

**Figure 3.** Quiver diagram of ADHM. The holographic dual geometry to ADHM is given by AdS4 × S 7/ZNf . The SE7 metric of the background in this case is given by (4.2) where the direction of the M-theory circle is now identified with the angle ϕ2, which has periodicity ϕ2 ∼ ϕ2 + 4π Nf . (4.16) The remaining angles have now the following ranges: θ ∈ [0, π/2], θ1,2 ∈ [0, π], {φ, ϕ1, ρ} ∈ [0, 2π) and the Hamiltonian function in thi… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Quiver diagram of Q1,1,1/ZNf . The seven-dimensional Q1,1,1/ZNf metric of interest reads [39] ds 2 7 = 1 16 dξ + X 3 i=1 cos θi dϕi 2 + 1 8 X 3 i=1 dθ 2 i + sin2 θi dϕ 2 i , (4.25) where the S 2 coordinates have ranges θi ∈ [0, π], ϕi ∈ [0, 2π) and the fibre dir…

**Figure 5.** Figure 5: Quiver diagram of Q˜1,1,1/Zk. 4.3.2 Q1,1,1/Zk We now turn to a different Q1,1,1/Zk model with Chern-Simons levels k = (k, 0, −k, 0) and global symmetry U(1)R × SU(2)2 × U(1) studied in [43,44].15 In this case, the seven-dimensional Q1,1,1/Zk metric is given by (4.25) w…

**Figure 6.** Figure 6: Quiver diagram of V5,2/ZNf . In this case the relevant seven-dimensional SE metric is given by [46] ds 2 7 = 9 16 dξ + 1 2 cos α(dβ − cos θ1dϕ1 − cos θ2dϕ2) 2 + ds 2 Gr5,2 , (4.35) where ds 2 Gr5,2 = 3 32 4dα 2 + sin2 α(dβ − cos θ1dϕ1 − cos θ2dϕ2) 2 + (1 + cos2 α)(…

**Figure 7.** Figure 7: Quiver diagram of V5,2/Zk. fields ΦI are massless, whereas in the case of ABJM they are massive and can be integrated out at the level of the superpotential in the low energy limit. For this model we study the same case that was studied in [19,27] and thus take β ∼ β +…

**Figure 8.** Figure 8: Quiver diagram of M3,2 . with ρ1 ∈ [0, π], φ1 ∈ [0, 4π] and ψ1 ∈ [0, 2π/k). The classical M2-brane solution we consider is given by identifying the M-theory circle with ψ1, and as a result the corresponding Hamiltonian function reads hM = 3 8k sin2 µ . (4.51) The criti…

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Wilson loop in AdS$_3 \times S^3 \times T^4$ from quantum M2 brane
hep-th 2026-03 unverdicted novelty 6.0 of 10

The 1-loop M2-brane partition function for the Wilson loop in AdS3 x S3 x T4 equals kappa over sqrt(2 pi) with no higher-genus string corrections.

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Works this paper leans on

66 extracted references · 56 linked inside Pith · cited by 1 Pith paper

[14]

F. F. Gautason and J. van Muiden,Ensembles in M-theory and Holography, arXiv:2505.21633

arXiv
[36]

Giombi and A

S. Giombi and A. A. Tseytlin,Strong coupling expansion of circular Wilson loops and string theories in AdS5×S 5 and AdS4×CP 3,JHEP10(2020) 130, [arXiv:2007.08512]. 44

arXiv 2020
[1]

Aharony, O

O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena,N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,JHEP10(2008) 091, [arXiv:0806.1218]

arXiv 2008
[2]

Gaiotto and A

D. Gaiotto and A. Tomasiello,The gauge dual of Romans mass,JHEP01(2010) 015, [arXiv:0901.0969]

arXiv 2010
[3]

Guarino, D

A. Guarino, D. L. Jafferis, and O. Varela,String Theory Origin of Dyonic N=8 Supergravity and Its Chern-Simons Duals,Phys. Rev. Lett.115(2015), no. 9 091601, [arXiv:1504.08009]

arXiv 2015
[4]

Fluder and J

M. Fluder and J. Sparks,D2-brane Chern-Simons theories: F-maximization = a-maximization,JHEP01(2016) 048, [arXiv:1507.05817]

arXiv 2016
[5]

M. J. Duff, P. S. Howe, T. Inami, and K. S. Stelle,Superstrings in D=10 from Supermembranes in D=11,Phys. Lett. B191(1987) 70

1987
[6]

Aharony, D

O. Aharony, D. Jafferis, A. Tomasiello, and A. Zaffaroni,Massive type IIA string theory cannot be strongly coupled,JHEP11(2010) 047, [arXiv:1007.2451]

arXiv 2010

Show all 66 references

[7]

Pestun,Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun

V. Pestun,Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys.313(2012) 71–129, [arXiv:0712.2824]

2012 arXiv
[8]

Kapustin, B

A. Kapustin, B. Willett, and I. Yaakov,Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,JHEP03(2010) 089, [arXiv:0909.4559]

2010 arXiv
[9]

N. Hama, K. Hosomichi, and S. Lee,Notes on SUSY Gauge Theories on Three-Sphere, JHEP03(2011) 127, [arXiv:1012.3512]

2011 arXiv
[10]

J. M. Maldacena,Wilson loops in large N field theories,Phys. Rev. Lett.80(1998) 4859–4862, [hep-th/9803002]

1998 arXiv
[11]

Drukker, D

N. Drukker, D. J. Gross, and A. A. Tseytlin,Green-Schwarz string in AdS(5) x S**5: Semiclassical partition function,JHEP04(2000) 021, [hep-th/0001204]

2000 arXiv
[12]

Giombi and A

S. Giombi and A. A. Tseytlin,Wilson Loops at Large N and the Quantum M2-Brane,Phys. Rev. Lett.130(2023), no. 20 201601, [arXiv:2303.15207]

2023 arXiv
[13]

Farquet and J

D. Farquet and J. Sparks,Wilson loops and the geometry of matrix models in AdS4/CFT3, JHEP01(2014) 083, [arXiv:1304.0784]

2014 arXiv
[15]

Klemm, M

A. Klemm, M. Marino, M. Schiereck, and M. Soroush, Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach,Z. Naturforsch. A68(2013), no. 1-2 178–209, [arXiv:1207.0611]

2013 arXiv
[16]

D. L. Jafferis,The Exact Superconformal R-Symmetry Extremizes Z,JHEP05(2012) 159, [arXiv:1012.3210]

2012 arXiv
[17]

Drukker, M

N. Drukker, M. Marino, and P. Putrov,From weak to strong coupling in ABJM theory, Commun. Math. Phys.306(2011) 511–563, [arXiv:1007.3837]. 43

2011 arXiv
[18]

C. P. Herzog, I. R. Klebanov, S. S. Pufu, and T. Tesileanu,Multi-Matrix Models and Tri-Sasaki Einstein Spaces,Phys. Rev. D83(2011) 046001, [arXiv:1011.5487]

2011 arXiv
[19]

Martelli and J

D. Martelli and J. Sparks,The large N limit of quiver matrix models and Sasaki-Einstein manifolds,Phys. Rev. D84(2011) 046008, [arXiv:1102.5289]

2011 arXiv
[20]

D. L. Jafferis, I. R. Klebanov, S. S. Pufu, and B. R. Safdi,Towards the F-Theorem: N=2 Field Theories on the Three-Sphere,JHEP06(2011) 102, [arXiv:1103.1181]

2011 arXiv
[21]

Chen-Lin, J

X. Chen-Lin, J. Gordon, and K. Zarembo,N= 2∗super-Yang-Mills theory at strong coupling,JHEP11(2014) 057, [arXiv:1408.6040]

2014 arXiv
[22]

Marino and P

M. Marino and P. Putrov,ABJM theory as a Fermi gas,J. Stat. Mech.1203(2012) P03001, [arXiv:1110.4066]

2012 arXiv
[23]

Bobev, P.-J

N. Bobev, P.-J. De Smet, J. Hong, V. Reys, and X. Zhang,An Airy tale at large N,JHEP 07(2025) 123, [arXiv:2502.04606]

2025 arXiv
[24]

H. Fuji, S. Hirano, and S. Moriyama,Summing Up All Genus Free Energy of ABJM Matrix Model,JHEP08(2011) 001, [arXiv:1106.4631]

2011 arXiv
[25]

Mezei and S

M. Mezei and S. S. Pufu,Three-sphere free energy for classical gauge groups,JHEP02 (2014) 037, [arXiv:1312.0920]

2014 arXiv
[26]

Grassi and M

A. Grassi and M. Marino,M-theoretic matrix models,JHEP02(2015) 115, [arXiv:1403.4276]

2015 arXiv
[27]

Cheon, H

S. Cheon, H. Kim, and N. Kim,Calculating the partition function of N=2 Gauge theories onS 3 and AdS/CFT correspondence,JHEP05(2011) 134, [arXiv:1102.5565]

2011 arXiv
[28]

Geukens and J

S. Geukens and J. Hong,Subleading analysis for S3 partition functions ofN= 2 holographic SCFTs,JHEP06(2024) 190, [arXiv:2405.00845]

2024 arXiv
[29]

Amariti, C

A. Amariti, C. Klare, and M. Siani,The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals,JHEP10(2012) 019, [arXiv:1111.1723]

2012 arXiv
[30]

D. Gang, C. Hwang, S. Kim, and J. Park,Tests of AdS4/CFT3 correspondence forN= 2 chiral-like theory,JHEP02(2012) 079, [arXiv:1111.4529]

2012 arXiv
[31]

Bergshoeff, E

E. Bergshoeff, E. Sezgin, and P. K. Townsend,Supermembranes and Eleven-Dimensional Supergravity,Phys. Lett. B189(1987) 75–78

1987
[32]

Astesiano, P

D. Astesiano, P. Bomans, F. F. Gautason, V. G. M. Puletti, and A. Nix,Wilson loops and spherical branes,SciPost Phys.18(2025), no. 2 050, [arXiv:2407.07830]

2025 arXiv
[33]

Cassia and K

L. Cassia and K. Hristov,Constant maps in equivariant topological strings and geometric modeling of fluxes,arXiv:2502.20444
[34]

Drukker, M

N. Drukker, M. Marino, and P. Putrov,Nonperturbative aspects of ABJM theory,JHEP11 (2011) 141, [arXiv:1103.4844]

2011 arXiv
[35]

Hatsuda, S

Y. Hatsuda, S. Moriyama, and K. Okuyama,Instanton Bound States in ABJM Theory, JHEP05(2013) 054, [arXiv:1301.5184]

2013 arXiv
[37]

Okuyama,Wilson loops in 3dN= 4 SQCD from Fermi gas,JHEP11(2016) 156, [arXiv:1610.02116]

K. Okuyama,Wilson loops in 3dN= 4 SQCD from Fermi gas,JHEP11(2016) 156, [arXiv:1610.02116]

2016 arXiv
[38]

Benini, C

F. Benini, C. Closset, and S. Cremonesi,Chiral flavors and M2-branes at toric CY4 singularities,JHEP02(2010) 036, [arXiv:0911.4127]

2010 arXiv
[39]

B. E. W. Nilsson and C. N. Pope,Hopf Fibration of Eleven-dimensional Supergravity,Class. Quant. Grav.1(1984) 499

1984
[40]

S. M. Hosseini,Large-NFree Energy of ChiralN= 2Chern-Simons-Matter Theories, arXiv:2510.24837
[41]

Franco, I

S. Franco, I. R. Klebanov, and D. Rodriguez-Gomez,M2-branes on Orbifolds of the Cone over Q**1,1,1,JHEP08(2009) 033, [arXiv:0903.3231]

2009 arXiv
[42]

Franco, A

S. Franco, A. Hanany, J. Park, and D. Rodriguez-Gomez,Towards M2-brane Theories for Generic Toric Singularities,JHEP12(2008) 110, [arXiv:0809.3237]

2008 arXiv
[43]

Aganagic,A Stringy Origin of M2 Brane Chern-Simons Theories,Nucl

M. Aganagic,A Stringy Origin of M2 Brane Chern-Simons Theories,Nucl. Phys. B835 (2010) 1–28, [arXiv:0905.3415]

2010 arXiv
[44]

Kim and N

H. Kim and N. Kim,Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields,JHEP05(2012) 152, [arXiv:1202.6637]

2012 arXiv
[45]

D. L. Jafferis,Quantum corrections toN= 2Chern-Simons theories with flavor and their AdS4 duals,JHEP08(2013) 046, [arXiv:0911.4324]

2013 arXiv
[46]

Bergman and C

A. Bergman and C. P. Herzog,The Volume of some nonspherical horizons and the AdS / CFT correspondence,JHEP01(2002) 030, [hep-th/0108020]

2002 arXiv
[47]

E. W. Barnes,The theory of the double gamma function,Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character196(1901) 265–387

1901
[48]

A. G. Bytsko and J. Teschner,Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model,J. Phys. A39(2006) 12927–12981, [hep-th/0602093]

2006 arXiv
[49]

Martelli and J

D. Martelli and J. Sparks,AdS4/CFT3 duals from M2-branes at hypersurface singularities and their deformations,JHEP12(2009) 017, [arXiv:0909.2036]

2009 arXiv
[50]

Martelli and J

D. Martelli and J. Sparks,Moduli spaces of Chern-Simons quiver gauge theories and AdS(4)/CFT(3),Phys. Rev. D78(2008) 126005, [arXiv:0808.0912]

2008 arXiv
[51]

Bobev, P

N. Bobev, P. Bomans, F. F. Gautason, and V. S. Min,Marginal deformations from type IIA supergravity,SciPost Phys.10(2021), no. 6 140, [arXiv:2103.02038]

2021 arXiv
[52]

K. A. Intriligator and B. Wecht,The Exact superconformal R symmetry maximizes a,Nucl. Phys. B667(2003) 183–200, [hep-th/0304128]

2003 arXiv
[53]

Henningson and K

M. Henningson and K. Skenderis,The Holographic Weyl anomaly,JHEP07(1998) 023, [hep-th/9806087]

1998 arXiv
[54]

Passias, D

A. Passias, D. Prins, and A. Tomasiello,A massive class ofN= 2AdS4 IIA solutions, JHEP10(2018) 071, [arXiv:1805.03661]. 45

2018 arXiv
[55]

Singh,Bosonic Fluctuations in Semiclassically Quantized Strings, Master’s thesis, University of Iceland, 2023

D. Singh,Bosonic Fluctuations in Semiclassically Quantized Strings, Master’s thesis, University of Iceland, 2023

2023
[56]

Cvetic, H

M. Cvetic, H. Lu, C. N. Pope, and K. S. Stelle,T duality in the Green-Schwarz formalism, and the massless / massive IIA duality map,Nucl. Phys. B573(2000) 149–176, [hep-th/9907202]

2000 arXiv
[57]

F. F. Gautason and V. G. M. Puletti,Precision holography for 5D Super Yang-Mills,JHEP 03(2022) 018, [arXiv:2111.15493]

2022 arXiv
[58]

L. J. Romans,New Compactifications of ChiralN= 2d= 10Supergravity,Phys. Lett. B 153(1985) 392–396

1985
[59]

J. P. Gauntlett, D. Martelli, J. Sparks, and D. Waldram,Sasaki-Einstein metrics on S**2 x S**3,Adv. Theor. Math. Phys.8(2004), no. 4 711–734, [hep-th/0403002]

2004 arXiv
[60]

Hong and J

J. Hong and J. T. Liu,Subleading corrections to the S3 free energy of necklace quiver theories dual to massive IIA,JHEP11(2021) 183, [arXiv:2103.17033]

2021 arXiv
[61]

Gaiotto and A

D. Gaiotto and A. Tomasiello,Perturbing gauge/gravity duals by a Romans mass,J. Phys. A42(2009) 465205, [arXiv:0904.3959]

2009 arXiv
[62]

Bobev, P.-J

N. Bobev, P.-J. De Smet, F. F. Gautason, and A. Nix,Work in progress,
[63]

Cagnazzo, D

A. Cagnazzo, D. Sorokin, and L. Wulff,String instanton in AdS(4) x CP**3,JHEP05 (2010) 009, [arXiv:0911.5228]

2010 arXiv
[64]

F. F. Gautason, V. G. M. Puletti, and J. van Muiden,Quantized strings and instantons in holography,JHEP08(2023) 218, [arXiv:2304.12340]

2023 arXiv
[65]

Beccaria, S

M. Beccaria, S. Giombi, and A. A. Tseytlin,Instanton contributions to the ABJM free energy from quantum M2 branes,JHEP10(2023) 029, [arXiv:2307.14112]

2023 arXiv
[66]

F. F. Gautason and J. van Muiden,Localisation of the M2-brane,arXiv:2503.16597. 46

arXiv

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [14]

F. F. Gautason and J. van Muiden,Ensembles in M-theory and Holography, arXiv:2505.21633

arXiv

[2] [36]

Giombi and A

S. Giombi and A. A. Tseytlin,Strong coupling expansion of circular Wilson loops and string theories in AdS5×S 5 and AdS4×CP 3,JHEP10(2020) 130, [arXiv:2007.08512]. 44

arXiv 2020

[3] [1]

Aharony, O

O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena,N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,JHEP10(2008) 091, [arXiv:0806.1218]

arXiv 2008

[4] [2]

Gaiotto and A

D. Gaiotto and A. Tomasiello,The gauge dual of Romans mass,JHEP01(2010) 015, [arXiv:0901.0969]

arXiv 2010

[5] [3]

Guarino, D

A. Guarino, D. L. Jafferis, and O. Varela,String Theory Origin of Dyonic N=8 Supergravity and Its Chern-Simons Duals,Phys. Rev. Lett.115(2015), no. 9 091601, [arXiv:1504.08009]

arXiv 2015

[6] [4]

Fluder and J

M. Fluder and J. Sparks,D2-brane Chern-Simons theories: F-maximization = a-maximization,JHEP01(2016) 048, [arXiv:1507.05817]

arXiv 2016

[7] [5]

M. J. Duff, P. S. Howe, T. Inami, and K. S. Stelle,Superstrings in D=10 from Supermembranes in D=11,Phys. Lett. B191(1987) 70

1987

[8] [6]

Aharony, D

O. Aharony, D. Jafferis, A. Tomasiello, and A. Zaffaroni,Massive type IIA string theory cannot be strongly coupled,JHEP11(2010) 047, [arXiv:1007.2451]

arXiv 2010