pith. sign in

arxiv: 2606.30341 · v1 · pith:3K4YDUDBnew · submitted 2026-06-29 · ✦ hep-th

A note on the holographic consistency of DGKT-type vacua with h^(2,1)=0

Filippo Revello , Farah Verbeure This is my paper

Pith reviewed 2026-06-30 05:09 UTC · model grok-4.3

classification ✦ hep-th
keywords DGKT vacuaholographic constraintsscale-separated AdSmassive type IIAmoduli three-point functionsh^{2,1}=0orbifold geometriesstring compactifications
0
0 comments X

The pith

Cancellations satisfy holographic constraint in DGKT vacua with h^{2,1}=0

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

The paper examines whether a recently identified holographic constraint on three-point functions of scalar moduli in scale-separated AdS vacua continues to hold in more general DGKT constructions in massive type IIA. Starting from the known satisfaction of the constraint in the symmetric T^6/(Z3 x Z3) orbifold due to specific cancellations, the authors check several less symmetric geometries with nontrivial triple intersection numbers. They find that the cancellations continue to occur whenever h^{2,1} vanishes. A reader would care because this points toward the constraint being a robust feature of these vacua rather than an accident of high symmetry, potentially revealing a selection principle in string theory compactifications.

Core claim

The cancellations responsible for satisfying the holographic constraint on extremal three-point functions of scalar moduli in the original DGKT scenario persist across all examined examples of DGKT-type vacua with h^{2,1}=0, including those with reduced symmetry and more complicated triple-intersection numbers. This leads to the speculation that the conclusion holds more generally for all such vacua.

What carries the argument

The unexpected cancellations in the computation of three-point functions of scalar moduli that make the holographic constraint hold in the DGKT scenario.

If this is right

  • The holographic constraint is satisfied in DGKT vacua with h^{2,1}=0 regardless of the specific geometry details examined.
  • Less symmetric orbifolds and manifolds still exhibit the same pattern of cancellations.
  • The property may be tied to the vanishing of h^{2,1} rather than to the high degree of symmetry in the original example.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the pattern holds generally, it could imply that scale-separated AdS vacua in massive type IIA are always holographically consistent when h^{2,1}=0.
  • Examining whether the cancellations occur in non-DGKT flux vacua or in cases with nonzero h^{2,1} would test the scope of the observation.
  • The result suggests a possible connection between the topology of the internal manifold and the consistency of the dual CFT three-point functions.

Load-bearing premise

The examined less-symmetric geometries are representative of all possible cases with h^{2,1}=0.

What would settle it

Constructing or identifying a single DGKT-type vacuum with h^{2,1}=0 in which the three-point function cancellations fail to satisfy the holographic constraint would disprove the generality.

read the original abstract

Recent works have pointed out the existence of a holographic constraint on (extremal) three-point functions of scalar moduli in scale-separated AdS vacua. Moreover, it has been shown that this constraint is satisfied in the DGKT scenario in massive type IIA for the original $\mathbb{T}^6/(\mathbb{Z}_3 \times \mathbb{Z}_3)$ orbifold, as a result of a series of unexpected cancellations. We extend the analysis to more elaborate scenarios, involving geometries with less symmetry and more complicated triple-intersection numbers. Surprisingly, the cancellations persist in all examples with $h^{2,1}=0$, leading us to speculate this conclusion might hold more generally.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript extends prior checks of a holographic constraint on extremal three-point functions of scalar moduli in DGKT-type scale-separated AdS vacua of massive type IIA to geometries with h^{2,1}=0 but reduced symmetry and more complex triple-intersection numbers. Explicit calculations show that the same unexpected cancellations continue to hold, satisfying the constraint in all examined cases, leading the authors to speculate that the result may hold more generally.

Significance. The explicit verification in less-symmetric geometries strengthens the evidence that these vacua satisfy the holographic constraint. If the cancellations prove general for h^{2,1}=0, this would indicate a structural feature tied to the topology rather than symmetry, providing a useful data point for understanding consistency conditions in scale-separated AdS solutions.

major comments (1)
  1. [Abstract, paragraph 3] Abstract, paragraph 3 (and concluding discussion): the extrapolation that the cancellations 'might hold more generally' for all h^{2,1}=0 cases rests on the unverified assumption that the finite set of less-symmetric geometries is representative. No general argument, underlying mechanism, or proof is supplied to support this beyond the explicit examples.
minor comments (2)
  1. Clarify in the introduction or methods section how the new geometries were selected and why they constitute a sufficient test of reduced symmetry.
  2. List the explicit triple-intersection numbers and flux quanta for each new example in a table to facilitate independent verification.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and recommendation of minor revision. We agree that the language in the abstract and conclusion requires clarification to avoid overstating the scope of our explicit calculations.

read point-by-point responses

  1. Referee: [Abstract, paragraph 3] Abstract, paragraph 3 (and concluding discussion): the extrapolation that the cancellations 'might hold more generally' for all h^{2,1}=0 cases rests on the unverified assumption that the finite set of less-symmetric geometries is representative. No general argument, underlying mechanism, or proof is supplied to support this beyond the explicit examples.

    Authors: We acknowledge that the statement is based solely on the explicit examples computed in the paper and does not include a general argument or proof. The original text already qualifies the claim as a speculation, but we agree that the wording can be tightened. We will revise the abstract and concluding discussion to state more explicitly that the cancellations are observed to persist in all examined geometries with h^{2,1}=0 (including those with reduced symmetry and more complex triple intersections), while making clear that no general proof is provided. This change will be implemented in the next version. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit computations in sample geometries verified against external constraint

full rationale

The paper extends prior explicit checks of three-point function cancellations to additional DGKT-type vacua with h^{2,1}=0 and reduced symmetry, reporting that the cancellations continue to hold in these cases. These are presented as observed numerical features matched to an external holographic constraint cited from recent works, with the generality left as an unproven speculation. No step equates a claimed prediction to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames an input as a derived result. The analysis remains self-contained against the external benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the claim rests on standard string theory compactification techniques and the holographic constraint from prior works.

pith-pipeline@v0.9.1-grok · 5645 in / 1062 out tokens · 24900 ms · 2026-06-30T05:09:36.332455+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

66 extracted references · 65 canonical work pages · 25 internal anchors

  1. [1]

    Coudarchet,Hiding the extra dimensions: A review on scale separation in string theory, Phys

    T. Coudarchet,Hiding the extra dimensions: A review on scale separation in string theory, Phys. Rept.1064(2024) 1 [2311.12105]

    work page arXiv 2024

  2. [2]

    F. F. Gautason, M. Schillo, T. Van Riet and M. Williams,Remarks on scale separation in flux vacua,JHEP03(2016) 061 [1512.00457]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  3. [3]

    Cribiori, G

    N. Cribiori, G. Dall’agata and F. Farakos,Weak gravity versus de Sitter,JHEP04(2021) 046 [2011.06597]

    work page arXiv 2021

  4. [4]

    Cribiori and G

    N. Cribiori and G. Dall’Agata,Weak gravity versus scale separation,JHEP06(2022) 006 [2203.05559]

    work page arXiv 2022

  5. [5]

    Montero, M

    M. Montero, M. Rocek and C. Vafa,Pure supersymmetric AdS and the Swampland,JHEP01 (2023) 094 [2212.01697]

    work page arXiv 2023

  6. [6]

    Cribiori, F

    N. Cribiori, F. Farakos and N. Liatsos,On scale-separated supersymmetric AdS 2 flux vacua, Eur. Phys. J. C85(2025) 213 [2411.04932]

    work page arXiv 2025

  7. [7]

    Scale-separated vacua with extended supersymmetry

    N. Cribiori, F. Farakos and A. Zarafonitis,Scale-separated vacua with extended supersymmetry, 2604.26755

    work page internal anchor Pith review Pith/arXiv arXiv

  8. [8]

    de Sitter Vacua in String Theory

    S. Kachru, R. Kallosh, A. D. Linde and S. P. Trivedi,De Sitter vacua in string theory,Phys. Rev. D68(2003) 046005 [hep-th/0301240]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  9. [9]

    Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications

    V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo,Systematics of moduli stabilisation in Calabi-Yau flux compactifications,JHEP03(2005) 007 [hep-th/0502058]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  10. [10]

    J. P. Conlon, F. Quevedo and K. Suruliz,Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking,JHEP08(2005) 007 [hep-th/0505076]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  11. [11]

    Type IIA Moduli Stabilization

    O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor,Type IIA moduli stabilization,JHEP07 (2005) 066 [hep-th/0505160]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  12. [12]

    P. G. Camara, A. Font and L. E. Ibanez,Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold,JHEP09(2005) 013 [hep-th/0506066]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  13. [13]

    Cribiori, D

    N. Cribiori, D. Junghans, V. Van Hemelryck, T. Van Riet and T. Wrase,Scale-separated AdS4 vacua of IIA orientifolds and M-theory,Phys. Rev. D104(2021) 126014 [2107.00019]

    work page arXiv 2021

  14. [14]

    Carrasco, T

    R. Carrasco, T. Coudarchet, F. Marchesano and D. Prieto,New families of scale separated vacua,JHEP11(2023) 094 [2309.00043]

    work page arXiv 2023

  15. [15]

    Van Hemelryck,Weak G2 manifolds and scale separation in M-theory from type IIA backgrounds,Phys

    V. Van Hemelryck,Weak G2 manifolds and scale separation in M-theory from type IIA backgrounds,Phys. Rev. D110(2024) 106013 [2408.16609]

    work page arXiv 2024

  16. [16]

    Farakos, G

    F. Farakos, G. Tringas and T. Van Riet,No-scale and scale-separated flux vacua from IIA on G2 orientifolds,Eur. Phys. J. C80(2020) 659 [2005.05246]

    work page arXiv 2020

  17. [17]

    Farakos, M

    F. Farakos, M. Morittu and G. Tringas,On/off scale separation,JHEP10(2023) 067 [2304.14372]

    work page arXiv 2023

  18. [18]

    Farakos and G

    F. Farakos and G. Tringas,Integer dual dimensions in scale-separated AdS 3 from massive IIA, JHEP06(2025) 130 [2502.08215]

    work page arXiv 2025

  19. [19]

    Tringas,T-dualities and scale-separated AdS 3 in massless IIA on(X 6 ×S 1)/Z2,2603.26615

    G. Tringas,T-dualities and scale-separated AdS 3 in massless IIA on(X 6 ×S 1)/Z2,2603.26615. – 25 –

    work page arXiv

  20. [20]

    Van Hemelryck,Supersymmetric scale-separated AdS 3 orientifold vacua of type IIB,JHEP 10(2025) 109 [2502.04791]

    V. Van Hemelryck,Supersymmetric scale-separated AdS 3 orientifold vacua of type IIB,JHEP 10(2025) 109 [2502.04791]

    work page arXiv 2025

  21. [21]

    Z. Miao, M. Rajaguru, G. Tringas and T. Wrase,T-dualities and scale-separated AdS 3 in type I, 2509.12801

    work page arXiv

  22. [22]

    Tringas and T

    G. Tringas and T. Wrase,Classical scale-separated AdS 3 vacua in heterotic string theory, 2511.07781

    work page arXiv

  23. [23]

    Baines and T

    S. Baines and T. Van Riet,Smearing orientifolds in flux compactifications can be OK,Class. Quant. Grav.37(2020) 195015 [2005.09501]

    work page arXiv 2020

  24. [24]

    Marchesano, E

    F. Marchesano, E. Palti, J. Quirant and A. Tomasiello,On supersymmetric AdS 4 orientifold vacua,JHEP08(2020) 087 [2003.13578]

    work page arXiv 2020

  25. [25]

    Emelin, F

    M. Emelin, F. Farakos and G. Tringas,O6-plane backreaction on scale-separated Type IIA AdS 3 vacua,JHEP07(2022) 133 [2202.13431]

    work page arXiv 2022

  26. [26]

    Junghans,O-Plane Backreaction and Scale Separation in Type IIA Flux Vacua,Fortsch

    D. Junghans,O-Plane Backreaction and Scale Separation in Type IIA Flux Vacua,Fortsch. Phys.68(2020) 2000040 [2003.06274]

    work page arXiv 2020

  27. [27]

    Junghans,A note on O6 intersections in AdS flux vacua,JHEP02(2024) 126 [2310.17695]

    D. Junghans,A note on O6 intersections in AdS flux vacua,JHEP02(2024) 126 [2310.17695]

    work page arXiv 2024

  28. [28]

    Polchinski and E

    J. Polchinski and E. Silverstein,Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT, pp. 365–390. World Scientific, 8, 2009.0908.0756. 10.1142/9789814412551 0018

    work page doi:10.1142/9789814412551 2009

  29. [29]

    L. F. Alday and E. Perlmutter,Growing Extra Dimensions in AdS/CFT,JHEP08(2019) 084 [1906.01477]

    work page arXiv 2019

  30. [30]

    Bobev, M

    N. Bobev, M. David, J. Hong, V. Reys and X. Zhang,A compendium of logarithmic corrections in AdS/CFT,JHEP04(2024) 020 [2312.08909]

    work page arXiv 2024

  31. [31]

    Perlmutter,Rigorous Holographic Bound on AdS Scale Separation,Phys

    E. Perlmutter,Rigorous Holographic Bound on AdS Scale Separation,Phys. Rev. Lett.133 (2024) 061601 [2402.19358]

    work page arXiv 2024

  32. [32]

    J. P. Conlon and F. Quevedo,Putting the Boot into the Swampland,JHEP03(2019) 005 [1811.06276]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  33. [33]

    J. P. Conlon and F. Revello,Moduli Stabilisation and the Holographic Swampland,LHEP2020 (2020) 171 [2006.01021]

    work page arXiv 2020

  34. [34]

    On the Conformal Field Theory Duals of type IIA AdS_4 Flux Compactifications

    O. Aharony, Y. E. Antebi and M. Berkooz,On the Conformal Field Theory Duals of type IIA AdS(4) Flux Compactifications,JHEP02(2008) 093 [0801.3326]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  35. [35]

    J. P. Conlon, S. Ning and F. Revello,Exploring the holographic Swampland,JHEP04(2022) 117 [2110.06245]

    work page arXiv 2022

  36. [36]

    Apers, M

    F. Apers, M. Montero, T. Van Riet and T. Wrase,Comments on classical AdS flux vacua with scale separation,JHEP05(2022) 167 [2202.00682]

    work page arXiv 2022

  37. [37]

    Apers, J

    F. Apers, J. P. Conlon, S. Ning and F. Revello,Integer conformal dimensions for type IIa flux vacua,Phys. Rev. D105(2022) 106029 [2202.09330]

    work page arXiv 2022

  38. [38]

    The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies

    A. Herraez, L. E. Ibanez, F. Marchesano and G. Zoccarato,The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies,JHEP09(2018) 018 [1802.05771]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  39. [39]

    Marchesano and J

    F. Marchesano and J. Quirant,A Landscape of AdS Flux Vacua,JHEP12(2019) 110 [1908.11386]. – 26 –

    work page arXiv 2019

  40. [40]

    Arboleya, A

    ´A. Arboleya, A. Guarino and M. Morittu,Type II orientifold flux vacua in 3D,JHEP12(2024) 087 [2408.01403]

    work page arXiv 2024

  41. [41]

    Montero and I

    M. Montero and I. Valenzuela,Quantum corrections to DGKT and the Weak Gravity Conjecture,JHEP07(2025) 057 [2412.00189]

    work page arXiv 2025

  42. [42]

    Apers, M

    F. Apers, M. Montero and I. Valenzuela,Backtracking AdS flux vacua,JHEP03(2026) 161 [2506.03314]

    work page arXiv 2026

  43. [43]

    Apers,On the DGKT brane dual and its decoupling,2601.15093

    F. Apers,On the DGKT brane dual and its decoupling,2601.15093

    work page arXiv

  44. [44]

    Bedroya and P

    A. Bedroya and P. J. Steinhardt,Holography vs. Scale Separation,2509.25313

    work page arXiv

  45. [45]

    Arboleya, A

    ´A. Arboleya, A. Guarino, C. Rold´ an-Dom´ ınguez and G. Sudano,On the branes behind scale-separated AdS3 flux vacua,2606.14469

    work page arXiv

  46. [46]

    A Holographic Constraint on Scale Separation

    N. Bobev, H. Paul and F. Revello,Holographic Constraint on Scale Separation,Phys. Rev. Lett. 136(2026) 181601 [2512.11031]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  47. [47]

    Broken and restored: a holographic constraint for AdS vacua with orbifolds

    F. Revello and V. Van Hemelryck,Broken and restored: a holographic constraint for AdS vacua with orbifolds,2605.07464

    work page internal anchor Pith review Pith/arXiv arXiv

  48. [48]

    Revello and V

    F. Revello and V. Van Hemelryck,N= 1spectra, cubic coupling and the rigid fate of DGKT, To appear

  49. [49]

    On Slow-roll Moduli Inflation in Massive IIA Supergravity with Metric Fluxes

    R. Flauger, S. Paban, D. Robbins and T. Wrase,Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes,Phys. Rev. D79(2009) 086011 [0812.3886]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  50. [50]

    T. W. Grimm and J. Louis,The Effective action of N = 1 Calabi-Yau orientifolds,Nucl. Phys. B699(2004) 387 [hep-th/0403067]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  51. [51]

    T. W. Grimm and J. Louis,The Effective action of type IIA Calabi-Yau orientifolds,Nucl. Phys. B718(2005) 153 [hep-th/0412277]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  52. [52]

    Bobev and H

    N. Bobev and H. Paul,Holographic correlators beyond maximal supersymmetry,JHEP09 (2025) 087 [2505.20400]

    work page arXiv 2025

  53. [53]

    Perturbative search for dead-end CFTs

    Y. Nakayama,Perturbative search for dead-end CFTs,JHEP05(2015) 046 [1501.02280]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  54. [54]

    Multiplets of Superconformal Symmetry in Diverse Dimensions

    C. Cordova, T. T. Dumitrescu and K. Intriligator,Multiplets of Superconformal Symmetry in Diverse Dimensions,JHEP03(2019) 163 [1612.00809]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  55. [55]

    S. M. Chester, R. Mouland and J. van Muiden,Extremal couplings, graviton exchange, and gluon scattering in AdS,JHEP10(2025) 027 [2505.23948]

    work page arXiv 2025

  56. [56]

    S. M. Chester, R. Mouland, J. van Muiden and C. Virally,Extremal couplings and gluon scattering in M-theory,JHEP06(2026) 090 [2512.04057]

    work page arXiv 2026

  57. [57]

    Castro and P

    A. Castro and P. J. Martinez,Revisiting extremal couplings in AdS/CFT,JHEP12(2024) 157 [2409.15410]

    work page arXiv 2024

  58. [58]

    Extremal Correlators in the AdS/CFT Correspondence

    E. D’Hoker, D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli,Extremal correlators in the AdS / CFT correspondence,hep-th/9908160

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [59]

    Aprile, J

    F. Aprile, J. M. Drummond, P. Heslop, H. Paul, F. Sanfilippo, M. Santagata et al.,Single particle operators and their correlators in freeN= 4 SYM,JHEP11(2020) 072 [2007.09395]

    work page arXiv 2020

  60. [60]

    Comment on the Generation Number in Orbifold Compactifications

    J. Erler and A. Klemm,Comment on the generation number in orbifold compactifications, Commun. Math. Phys.153(1993) 579 [hep-th/9207111]. – 27 –

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  61. [61]

    Toroidal Orbifolds: Resolutions, Orientifolds and Applications in String Phenomenology

    S. Reffert,Toroidal Orbifolds: Resolutions, Orientifolds and Applications in String Phenomenology, Ph.D. thesis, Munich U., 2006.hep-th/0609040

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  62. [62]

    The Geometer's Toolkit to String Compactifications

    S. Reffert,The Geometer’s Toolkit to String Compactifications, inConference on String and M Theory Approaches to Particle Physics and Cosmology, 6, 2007,0706.1310

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  63. [63]

    Superconformal Symmetry in Three-dimensions

    J.-H. Park,Superconformal symmetry in three-dimensions,J. Math. Phys.41(2000) 7129 [hep-th/9910199]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  64. [64]

    E. I. Buchbinder, S. M. Kuzenko and I. B. Samsonov,Superconformal field theory in three dimensions: Correlation functions of conserved currents,JHEP06(2015) 138 [1503.04961]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  65. [65]

    N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory

    H. Osborn,N=1 superconformal symmetry in four-dimensional quantum field theory,Annals Phys.272(1999) 243 [hep-th/9808041]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  66. [66]

    Bootstrapping minimal $\mathcal{N}=1$ superconformal field theory in three dimensions

    J. Rong and N. Su,Bootstrapping the minimalN= 1 superconformal field theory in three dimensions,JHEP06(2021) 154 [1807.04434]. – 28 –

    work page internal anchor Pith review Pith/arXiv arXiv 2021