Pith. sign in

REVIEW 5 major objections 8 minor 1 cited by

Class $\mathcal{S}$ superconformal indices from maximal supergravity

T0 review · 5 major / 8 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A consistent truncation of eleven-dimensional supergravity on the wrapped-M5-brane geometry determines the complete universal light spectrum of the dual class S theory and yields its superconformal index, matching known large-N field…

desk verdict A likely important result for holographic class S, but the completeness claim rests on an unproved exclusion of non-universal Maass eigenvalues in footnote 44. read the letter →

arxiv 2411.16837 v2 pith:S6N6AOAK submitted 2024-11-25 hep-th gr-qcmath-phmath.MP

Ritabrata Bhattacharya , Abhay Katyal , Oscar Varela This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP PACS 04.65.+e11.25.Tq
keywords superconformalindexclassStheoriesmaximalsupergravityconsistenttruncationM5-branesexceptionalgeneralisedgeometryMaassLaplacianAdS/CFTcorrespondence
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

This paper establishes that $D=11$ supergravity on the geometry obtained by wrapping M5-branes on a Riemann surface admits a consistent truncation to a new five-dimensional maximal supergravity, one that gauges the local scaling symmetry as well as a group containing $\mathrm{ISO}(5)$. The truncation fixes the complete universal spectrum of light operators in the dual four-dimensional $\mathcal{N}=2$ theory of class $\mathcal{S}$, organized into towers of superconformal multiplets. From the short multiplets in that spectrum, the authors compute the holographic superconformal index and match the known large-$N$ field-theory result in the Hall-Littlewood limit. This is presented as the first holographic derivation of a class $\mathcal{S}$ superconformal index and the first maximal truncation on a non-spherical, non-parallelisable internal geometry.

What carries the argument

The load-bearing object is the generalised frame (11) in exceptional generalised geometry, a repackaging of the fields of $D=11$ supergravity into $\mathrm{E}_{6(6)}$ multiplets, built from the local vielbeins of the Riemann surface $\Sigma$ and the Killing vectors of the four-sphere fibre together with the fibration element (13). Its generalised torsion is constant and reproduces the embedding tensor (1) with (4), (5), which is the criterion for a consistent truncation to maximal supergravity. On the spectrum side, the Maass Laplacian $D_n$ on $\Sigma$ supplies the universal eigenvalues (19) with multiplicities (20), and the graviton eigenvalue problem separates into the hypergeometric equation (17); the resulting masses (22) determine the towers (24). States at KK level $k\ge 1$ are generated by tensoring the five-dimensional $N=8$ supergravity multiplet with the graviton eigenstates, and the mass matrices are diagonalised level by level. The superconformal index (26) is then evaluated by identifying the short multiplets in these towers.

What would settle it

Compute the large-$N$ Schur index from the finite-$N$ field-theory results of [5] and compare it with the Schur limit of (29); any mismatch would falsify the claimed holographic index.

Watch

Extended reading notes

Core claim

The central claim is that the maximal $N=8$ supergravity in five dimensions specified by the embedding tensor (1) with (4), (5) arises by consistent truncation of $D=11$ supergravity on the $\mathrm{AdS}_5 \times (\Sigma \rtimes S^4)$ solution of [6]. Consistency is shown through a generalised frame whose generalised torsion is constant and matches that embedding tensor, even though the internal space is neither spherical nor parallelisable and the frame is only locally defined. The truncation then controls the full Kaluza-Klein spectrum: at every KK level the light states assemble into the towers of $\mathfrak{su}(2,2|2)$ supermultiplets displayed in (24), with genus-dependent multiplicities supplied by the universal eigenvalues of the Maass Laplacian on $\Sigma$. Keeping only the short multiplets and summing their contributions yields the superconformal index (29), which reduces to the Hall-Littlewood index $I_{HL}=(g-1)\tau^4/(1-\tau^2)$ in agreement with the large-$N$ field-theory result of [5]. The paper therefore claims the first holographic match of a class $\mathcal{S}$ superconformal index.

Load-bearing premise

The argument assumes that the only wave modes that matter are the ones fixed by symmetry, and that the extra modes special to each particular Riemann surface, which the paper explicitly sets aside, do not contribute to the index.

Editorial extensions

If this is right

  • The index formula (29) supplies explicit large-$N$ predictions for the Schur, Macdonald and Coulomb branch limits of the class $\mathcal{S}$ index, to be compared with the finite-$N$ results of [5].
  • All light states of the $\mathrm{AdS}_5 \times (\Sigma \rtimes S^4)$ solution are accounted for by the universal towers (24), so no additional protected multiplets appear in the spectrum.
  • The genus dependence of the spectrum and index, encoded in the $(g-1)$ factors from the Maass Laplacian multiplicities, matches the expected dependence of the dual class $\mathcal{S}$ theory.
  • The consistent truncation provides a concrete higher-dimensional origin for trombone gaugings, the gaugings of the local scaling symmetry of the metric, with supersymmetric AdS vacua.
  • The same generalised-geometry construction is expected to apply to the related wrapped-M5-brane geometries considered in [9], potentially yielding holographic indices for the corresponding $\mathcal{N}=1$ SCFTs.

Reading between the lines

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

  • Going beyond the paper, the same algebraic spectrum (24) determines the subleading large-$N$ corrections to the index once the non-short multiplets' one-loop determinants are evaluated, a step the paper does not take.
  • The decision to disregard non-universal Maass eigenvalues amounts to the conjecture that the holographic index depends only on the genus through $g-1$; a surface-dependent correction would be a clear and testable violation.
  • If the Schur and Macdonald predictions from (29) match future field-theory computations, it would confirm that the protected-sector data of class $\mathcal{S}$ theories at large $N$ is fixed entirely by the generalised-geometry truncation, without needing explicit Maass eigenfunctions.
  • One could test the truncation directly by computing the KK spectrum on a specific genus-two surface numerically and checking whether any state outside the towers (24) lies in a short supermultiplet.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 8 minor

Summary. The paper constructs a new gauging of five-dimensional maximal supergravity with gauge group B2⋉ISO(5), including a trombone (local scaling) gauging, and shows that this theory arises as a consistent truncation of M-theory on the AdS5×(Σ⋊S4) geometry of Maldacena–Núñez, where Σ is a smooth Riemann surface of genus g≥2. Using exceptional generalized geometry, the authors propose a generalized frame whose torsion matches the embedding tensor, thereby establishing the truncation. They then use this truncation to derive the full "universal" Kaluza–Klein spectrum (24) of the D=11 solution, organized in multiplets of su(2,2|2), and compute the large-N superconformal index (29) of the dual class-S SCFT, finding agreement with the Hall–Littlewood limit computed by Gadde–Rastelli–Razamat–Yan. The paper claims this is the first holographic match of a class-S superconformal index.

Significance. If correct, the paper would be a substantial advance: it would provide the first consistent truncation to maximal supergravity on a non-spherical, non-parallelisable internal geometry, the first higher-dimensional origin of a trombone gauging with an AdS vacuum, and the first holographic derivation of a class-S superconformal index at large N. The paper is honest about its main gap: the construction of explicit Maass eigenfunctions on the compact surface is open, and the universal spectrum rests on an algebraic prescription for the matrix (TM)ΛΣ. The agreement with the known Hall–Littlewood result is a genuine external check and does give nontrivial support. The paper makes explicit falsifiable predictions for other index limits. However, the completeness claim for the spectrum, and hence for the index, is not proven; this is the crux of the evaluation.

major comments (5)
  1. [Universal spectrum, Eq. (24) and footnote [44]] The central claim that (24) is the complete universal spectrum and that (29) is the full holographic index depends on the assertion that the algebraic prescription fully determines the matrices (TM)ΛΣ without explicit Maass eigenfunctions, and on the disregard in footnote [44] of non-universal discrete eigenvalues of the Maass Laplacian (18). Since Eq. (22) maps every eigenvalue E of Dn to a KK mass, and since Table I shows that any short su(2,2|2) multiplet contributes to the index, a non-universal eigenvalue lying on the shortening conditions of [29] would add a contribution to (29). The paper does not prove that shortening can only occur for the universal eigenvalues (19); it only states the algebraic arguments are enough. This is a load-bearing gap: without a proof or a compelling rationale that non-universal eigenvalues cannot satisfy the shortening conditions, the "complete, universal" label and the "perfect agreement" are conditional.
  2. [M-theory uplift, text after Eq. (13)] The consistency of the truncation rests on the statement that "a lengthy calculation shows that the generalised torsion XMNP associated to our frame (11) with (12), (13) is constant, and indeed matches the embedding tensor (1) with (4), (5)". This is the foundational input for the entire spectrum computation, but no details or intermediate results are provided, and the frame is only defined in terms of local frames ex, e^x on Σ. The authors cite standard EGG results and note the parallel with local G-structure truncations. Given that this is the first truncation on a non-parallelisable generalized geometry and that the frame is local in a non-trivial sense, the reader cannot verify the claimed matching of the embedding tensor without the calculation. I would ask for at least the essential steps of this calculation or a clear statement of where it appears in a follow-up, since this is the point on which the existence of the maximal truncation rests.
  3. [Table I and Eq. (29)] The derivation of the single-letter index from Table I is only sketched. It is stated that "writing out the state content of the short multiplets in (24) with the help of [29], we identify the contributions summarised in Table I" and that "taking into account the genus-dependent multiplicity and the overall contributions from derivatives" yields (28). The contributions in Table I do not immediately sum to (28) without specifying the multiplicity (20) included in each row and the derivative counting. Since the final agreement with (30) depends on the coefficient (g−1) and the power τ4, a one-line check of the sum would strengthen the paper. As written, an important step in the claimed match is left to the reader.
  4. [Consistency of (19) with the R-symmetry range (21)] The universal eigenvalues Enj=(|n|−j)(|n|−j−1) are quoted from [34] with range j=0,...,|n|−1, and (20) gives genus-dependent multiplicities. This is a standard result for the Maass Laplacian on compact hyperbolic surfaces of the type considered (Dn is the Maass–Laplacian twisted by a flat U(1) connection of half-integer?/integer weight). The paper does not specify the regularity/automorphy conditions under which (19)–(21) hold, nor the weight of Dn as derived from the reduction. If the Maass Laplacian (18) is the one of weight n, then the universal eigenvalues (19) can be partly exceptional/subspace-dependent; also, for |n|=1, (21) gives only j=0 with eigenvalue 0, consistent with the dimension formula. This point should be clarified; the completeness of (24) depends on the exact statement of which eigenvalues of Dn are universal, and the cited reference [34] is a standard but specialized source. A precise statement of the spectral theorem used would make the argument checkable.
  5. [Universality of the g−1 factor and comparison with [5]] The final index (29) scales as (g−1). The authors claim agreement with the large-N Hall–Littlewood result (5.49) of [5] "after taking the plethystic exponential (and up to an overall sign)". The overall sign and the plethystic exponential are both non-trivial: the single-letter index (29) is negative in some ranges of fugacities (e.g., the ρ4σ4 term is positive but the denominator can change sign), and the relation between the single-letter index and the full index is a plethystic exponent. The paper should provide the actual comparison, including the sign convention and the exact match of the series, rather than a parenthetical. This is the central positive check of the paper, and it deserves a few lines of detail.
minor comments (8)
  1. [Abstract and Introduction] The abstract states "gauge group containing ISO(5)" and later the gauge group is stated as B2⋉ISO(5); the relation between these two statements is not explained in the Introduction. A sentence clarifying that B2 is a Borel subgroup of GL(2) acting on the translations would help.
  2. [Eq. (5)] The component ξ2ab6=−g3√−κ ǫab has an index structure that is not explicitly defined (a,b are SO(5) indices split as (a,α); ξxABC is in (2,84), so the constraints on the antisymmetrization [AB]C should be spelled out. Please define the independent components of ξ2ab6 in the same way as θij and θαβ6γ.
  3. [Eq. (7)] In the scalar potential (7), the first term contains g4 2 g−2 1 κ2, but g3 has been set equal to g2. It would be helpful to state explicitly that this is the specialization g2=g3 used for the potential, and to clarify the dependence on κ=0 case (which is presumably Minkowski or de Sitter, not AdS).
  4. [Notation for multiplets] The notation A2Ā2, B1B̄1, etc., is taken from [29], but the definition of the lowest-weight labels (e.g., A2Ā2[0;0](0;0)2) is not given in the paper. For a self-contained reading, a one-sentence definition or a pointer to the conventions of [29] should be included. Also, Eq. (9) is presented as a "mass spectrum" but later said to reproduce (for the first line) the N=4 result; the reader would benefit from a table of the superconformal multiplet labels with their quantum numbers.
  5. [Footnote [40]] The footnote mapping the scalar fields to [12] contains what appears to be a typo: "ϕ0here = 2λthere − φthere" should likely read "ϕ1here = 2λthere − φthere". Please check the mapping.
  6. [Eq. (14)] In the uplifted metric (14), the dilaton ϕ2 appears in the dx2+dy2 factor but the scalar sector described earlier set ϕ2=0 for the SO(1,1)^2 model. It would be clearer to state explicitly the range of validity of (14) with all axions and vectors set to zero.
  7. [References] Reference [34] (Elstrodt) is cited for the universal eigenvalues of the Maass Laplacian; if the authors rely on a more standard textbook statement (e.g., Iwaniec, Spectral Methods of Automorphic Forms), citing both would be more accessible to the physics readership.
  8. [Text near Eq. (30)] The sentence "in agreement with the large-N result (5.49) of [5] after taking the plethystic exponential (and up to an overall sign)" is too terse; the sign and normalization conventions should be spelled out. This is minor only because the claim is likely correct, but the present level of detail makes verification harder than necessary.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the class-S superconformal index is computed from an explicit consistent-truncation construction and checked against an external field-theory result, not fitted to it.

full rationale

The derivation chain is not circular. The embedding tensor (1) with (4),(5) is a free construction in five-dimensional maximal gauged supergravity; the generalized frame (11)-(13) is an explicit ansatz built from the Maldacena-Nunez solution as described in [13]; and the paper reports a direct calculation that the torsion is constant and equals that embedding tensor with g1=R^-1, g2=g3=R_Sigma^-1. No parameter is fitted to the field-theory index. The universal spectrum (24) is derived from the graviton eigenvalue problem (15)-(22) plus the algebraic method of [19-22]; the universal Maass eigenvalues (19) and multiplicities (20) come from external mathematics [34,35], and the shortening conditions come from the external reference [29]. The index (29) is then summed over short multiplets, and the Hall-Littlewood limit is compared with the large-N result (5.49) of [5] only as an after-the-fact check; the agreement is not used to select the spectrum or to fix any coupling. Self-citations [21,22,25,31] are to spectral methods and earlier truncation technology, not to a result that assumes the class-S index, so they do not import the paper's conclusion. The only flagged weakness is footnote 44, where the paper states: "In addition, Dn may have other discrete, non-universal (i.e. specific to each Σ) eigenvalues, which we disregard." This is a completeness gap: if those non-universal eigenvalues could lie on a shortening locus and contribute to (29), the claimed completeness of (24) would fail. That is a correctness/completeness risk, not a circular reduction: the claim would be false in that scenario, but it is not made true by construction. Therefore no circularity step meets the threshold of exhibiting a specific input-output equivalence.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central index result is derived from a new embedding tensor with chosen coupling constants and a standard spectral-theory input. The main load-bearing assumption not supplied by prior literature is that the algebraic spectral method is complete without explicit Maass eigenfunctions.

free parameters (2)
  • gauge coupling constants g1, g2, g3 = g1 = R^{-1}, g2 = g3 = R_Sigma^{-1}
    Introduced in the embedding tensor (5) to define the new gauging; the simplification g2 = g3 is made for the potential (7). These are chosen by hand rather than fitted to data, and they do not enter the final index formula (29).
  • Riemann surface curvature parameter kappa = -1
    The AdS vacuum (8) and the uplifted metric (14) are constructed for kappa = -1, the negative curvature case corresponding to genus g >= 2. The paper notes that kappa = 1 would make the embedding tensor complex.
assumptions (4)
  • domain assumption A constant generalised torsion is necessary and sufficient for a consistent truncation to maximal supergravity
    Used to prove the consistency of the truncation of the frame (11) to the D=5 N=8 supergravity. This criterion is adopted from [15,17].
  • standard math The universal eigenvalues (19) and multiplicities (20) of the Maass Laplacian on a compact Riemann surface of genus g >= 2
    Used to compute the graviton spectrum and the genus dependence; cited from [34,35].
  • domain assumption The superconformal index receives contributions only from short multiplets of su(2,2|2)
    Used to restrict the multiplets in (24) to those in table I when computing the index (28). This is standard from [4,29].
  • ad hoc to paper The algebraic prescription using (T^M)_LambdaSigma fully determines the complete KK spectrum despite the absence of explicit Maass eigenfunctions, and non-universal eigenvalues of the Maass Laplacian can be neglected
    Stated in the Universal Spectrum section after Eq. (23) and footnote [44]. This is the paper's own assumption with no proof given; it is load-bearing for the completeness of (24) and the index (29).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Class $\mathcal{S}$ superconformal indices from maximal supergravity." pith.science (2026). https://pith.science/paper/S6N6AOAK

@misc{pith2026241116837,
  author       = {Pith},
  title        = {Pith review of: Class $\mathcalS$ superconformal indices from maximal supergravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S6N6AOAK}},
  note         = {Machine review of arXiv:2411.16837}
}
abstract

We present a new gauging of maximal supergravity in five spacetime dimensions with gauge group containing ISO(5), involving the local scaling symmetry of the metric, and admitting a supersymmetric anti-de Sitter vacuum. We show this maximal supergravity to arise by consistent truncation of M-theory on the (non-spherical, non-parallelisable) six-dimensional geometry associated to a stack of $N$ M5-branes wrapped on a smooth Riemann surface. The existence of this truncation allows us to holographically determine the complete, universal spectrum of light operators of the dual four-dimensional $\mathcal{N}=2$ theory of class $\mathcal{S}$. We then compute holographically the superconformal index of the dual field theory at large-$N$, finding perfect agreement with previously known field theory results in specific limits.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Maximal $D=5$ trombone supergravity from M5-branes and $\mathrm{SU}(2)$-flavoured $\mathcal{N}=1$ class $\mathcal{S}$ operator spectra

    hep-th 2026-07 conditional novelty 6.0 of 10

    A single D=5 maximal trombone supergravity locally describes all BBBW M5-brane AdS5 vacua, and its U(1)_0-invariant KK spectrum on MN1 yields closed-form holographic operator dimensions for universal graviton, graviti...

Reference graph

Works this paper leans on

45 extracted references · 14 canonical work pages · cited by 1 Pith paper

  1. [5]

    Gadde, L

    A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, Com- mun. Math. Phys. 319 (2013), 147 [arXiv:1110.3740]

    arXiv 2013

  2. [29]

    Guarino, C

    A. Guarino, C. Sterckx and M. Trigiante, Phys. Rev. D 111 (2025) no.4, 046019 [arXiv:2410.23149]

    arXiv 2025

  3. [44]

    The parameters are a = 1 4 (2ℓ + 2 |n| + 3) + A, b = 1 4 (2ℓ + 2 |n| + 3) − A and c = ℓ + 3 2 , with A ≡ 1 4 √ 2L2M 2 + 4E − 4ℓ(ℓ + 1) − 2n2 + 9, where E is the separation constant

    work page

  4. [34]

    D’Hoker and J

    E. D’Hoker and J. Kaidi [arXiv:2208.07242]

    arXiv

  5. [1]

    Witten, Commun

    E. Witten, Commun. Math. Phys. 117 (1988), 353

    work page 1988

  6. [2]

    Bershadsky, C

    M. Bershadsky, C. Vafa and V. Sadov, Nucl. Phys. B 463 (1996), 420-434 [arXiv:hep-th/9511222]

    arXiv 1996

  7. [3]

    Gaiotto, JHEP 08 (2012), 034 [arXiv:0904.2715]

    D. Gaiotto, JHEP 08 (2012), 034 [arXiv:0904.2715]

    arXiv 2012

  8. [4]

    Kinney, J.M

    J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, Commun. Math. Phys. 275 (2007), 209 [hep-th/0510251]

    arXiv 2007

Show all 45 references
  1. [6]

    Maldacena and C

    J.M. Maldacena and C. N´ u˜ nez, Int. J. Mod. Phys. A 16 (2001), 822-855 [hep-th/0007018]

    2001 arXiv

  2. [7]

    H. Lin, O. Lunin and J.M. Maldacena, JHEP 10 (2004), 025 [hep-th/0409174]

    2004 arXiv

  3. [8]

    Gaiotto and J.M

    D. Gaiotto and J.M. Maldacena, JHEP 10 (2012), 189 [arXiv:0904.4466]

    2012 arXiv

  4. [9]

    I. Bah, C. Beem, N. Bobev and B. Wecht, Phys. Rev. D 85 (2012), 121901 [arXiv:1112.5487]

    2012 arXiv

  5. [10]

    Ferrero, J.P

    P. Ferrero, J.P. Gauntlett, J.M. P´ erez Ipi˜ na, D. Martelli and J. Sparks, Phys. Rev. Lett. 126 (2021) no.11, 111601 [arXiv:2011.10579]

    2021 arXiv

  6. [11]

    I. Bah, F. Bonetti, R. Minasian and E. Nardoni, Phys. Rev. Lett. 127 (2021) no.21, 211601 [arXiv:2105.11567]

    2021 arXiv

  7. [12]

    Cheung, J.P

    K.C.M. Cheung, J.P. Gauntlett and C. Rosen, Class. Quant. Grav. 36 (2019) 22, 225003 [arXiv:1906.08900]

    2019 arXiv

  8. [13]

    Each entry in (11) is a generalised vector of the form V = (v,ω,σ ), withv a vector,ω a two-form andσ a five-form on Σ ⋊S4

    leads us to consider a generalised frame ˆEM = ( ˆEx, ˆExi, ˆEi, ˆEij ) , (11) with indices x = 1, 2, i = 1,..., 5 as above. Each entry in (11) is a generalised vector of the form V = (v,ω,σ ), withv a vector,ω a two-form andσ a five-form on Σ ⋊S4. To specify these, we introduc...

  9. [14]

    Cassani, G

    D. Cassani, G. Josse, M. Petrini and D. Waldram, JHEP 11 (2019), 017 [arXiv:1907.06730]

    2019 arXiv

  10. [15]

    Nastase, D

    H. Nastase, D. Vaman and P. van Nieuwenhuizen, Phys. Lett. B 469 (1999), 96-102 [hep-th/9905075]

    1999 arXiv

  11. [16]

    K. Lee, C. Strickland-Constable and D. Waldram, Fortsch. Phys. 65 (2017) 10, 1700048 [arXiv:1401.3360]

    2017 arXiv

  12. [17]

    Guarino, D.L

    A. Guarino, D.L. Jafferis and O. Varela, Phys. Rev. Lett. 115 (2015) no.9, 091601 [arXiv:1504.08009]

    2015 arXiv

  13. [18]

    Hohm and H

    O. Hohm and H. Samtleben, JHEP 01 (2015), 131 [arXiv:1410.8145]

    2015 arXiv

  14. [19]

    Inverso, H

    G. Inverso, H. Samtleben and M. Trigiante, Phys. Rev. D 95 (2017) no.6, 066020 [arXiv:1612.05123]

    2017 arXiv

  15. [20]

    Malek and H

    E. Malek and H. Samtleben, Phys. Rev. Lett. 124 (2020) no.10, 101601 [arXiv:1911.12640]

    2020 arXiv

  16. [21]

    Malek and H

    E. Malek and H. Samtleben, Phys. Rev. D 102 (2020) no.10, 106016 [arXiv:2009.03347]

    2020 arXiv

  17. [22]

    Varela, JHEP 04 (2021), 283 [arXiv:2010.09743]

    O. Varela, JHEP 04 (2021), 283 [arXiv:2010.09743]

    2021 arXiv

  18. [23]

    Ces` aro and O

    M. Ces` aro and O. Varela, JHEP 03 (2021), 138 [arXiv:2012.05249]

    2021 arXiv

  19. [24]

    de Wit, H

    B. de Wit, H. Samtleben and M. Trigiante, Nucl. Phys. B 716 (2005), 215-247 [arXiv:hep-th/0412173]

    2005 arXiv

  20. [25]

    Le Diffon and H

    A. Le Diffon and H. Samtleben, Nucl. Phys. B 811 (2009), 1-35 [arXiv:0809.5180]

    2009 arXiv

  21. [26]

    Blair, M

    C.D.A. Blair, M. Pico and O. Varela, JHEP 09 (2024), 065 [arXiv:2407.01298]

    2024 arXiv

  22. [27]

    Andrianopoli, F

    L. Andrianopoli, F. Cordaro, P. Fr´ e and L. Gualtieri, Class. Quant. Grav. 18 (2001), 395 [hep-th/0009048]

    2001 arXiv

  23. [28]

    Gunaydin, L.J

    M. Gunaydin, L.J. Romans and N.P. Warner, Nucl. Phys. B 272 (1986), 598

    1986

  24. [30]

    Cordova, T.T

    C. Cordova, T.T. Dumitrescu and K. Intriligator, JHEP 03 (2019), 163 [arXiv:1612.00809]

    2019 arXiv

  25. [31]

    Coimbra, C

    A. Coimbra, C. Strickland-Constable and D. Waldram, JHEP 02 (2014), 054 [arXiv:1112.3989]

    2014 arXiv

  26. [32]

    Gauntlett and O

    J.P. Gauntlett and O. Varela, Phys. Rev. D 76 (2007), 126007 [arXiv:0707.2315]

    2007 arXiv

  27. [33]

    Bachas and J

    C. Bachas and J. Estes, JHEP 06 (2011), 005 [arXiv:1103.2800]

    2011 arXiv

  28. [35]

    Elstrodt, Math

    J. Elstrodt, Math. Ann. 203, 4 (1973), 295

    1973

  29. [36]

    Shimura, Princeton University Press (1971)

    G. Shimura, Princeton University Press (1971)

    1971

  30. [37]

    Hohm and H

    O. Hohm and H. Samtleben, Phys. Rev. Lett. 111 (2013), 231601 [arXiv:1308.1673]

    2013 arXiv

  31. [38]

    K. Chen, M. Gutperle and C.F. Uhlemann, JHEP 06 (2019), 139 [arXiv:1903.07109]

    2019 arXiv

  32. [39]

    Cassani, G

    D. Cassani, G. Josse, M. Petrini and D. Waldram, JHEP 02 (2021), 232 [arXiv:2011.04775]

    2021 arXiv

  33. [40]

    We respectively denote half-maximal supersymmetry by N = 4 and N = 2 in 5d supergravity and 4d field theory

  34. [41]

    This model matches (3.7), (3.8) of [12], with ϕ0here = λthere + 2φthere, ϕ0here = 2 λthere − φthere, κhere = lthere, g1here = g2here = gthere and everything else set to zero

  35. [42]

    Our notation for the su(2, 2|2) supermultiplets is as in [29], with states denoted [ j1; j2](ℓ;n) ∆ , where jthere = 2j1here, ¯jthere = 2j2here, Rthere = 2ℓhere, rthere = 2nhere

  36. [43]

    For ϕ2 = 0, this agrees with (5.36) of [13] with RΣ = R and e2ϕ0here = e2ϕ1here = √ 2 Σ − 1 there

  37. [45]

    specific to each Σ) eigenvalues, which we disregard

    In addition, Dn may have other discrete, non-universal (i.e. specific to each Σ) eigenvalues, which we disregard

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.