$\mathcal{N}=1$ spectra, cubic couplings and the rigid fate of DGKT

Filippo Revello; Vincent Van Hemelryck

arxiv: 2607.00789 · v1 · pith:OJY3XIMPnew · submitted 2026-07-01 · ✦ hep-th

mathcal{N}=1 spectra, cubic couplings and the rigid fate of DGKT

Filippo Revello , Vincent Van Hemelryck This is my paper

Pith reviewed 2026-07-02 09:27 UTC · model grok-4.3

classification ✦ hep-th

keywords DGKT vacuaCalabi-Yau threefoldsholographic constraintcubic couplingsN=1 supergravityrigid manifoldscomplex structure moduliAdS vacua

0 comments

The pith

DGKT vacua satisfy the holographic constraint on cubic couplings only for rigid Calabi-Yau threefolds 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 analyzes supersymmetric DGKT compactifications of type IIA string theory on Calabi-Yau threefolds and applies a recently proposed holographic constraint involving cubic couplings. It establishes that this constraint holds precisely when the threefold is rigid, meaning it has no complex structure moduli so that h^{2,1} vanishes. The authors derive general relations in four-dimensional N=1 supergravity showing that extremal cubic couplings arise from third derivatives of a real Kähler-invariant superpotential and that the Hessian eigenvalues determine conformal dimensions of dual operators. In the DGKT setting these relations imply vanishing couplings in the Kähler plus universal sector but non-vanishing ones in the complex structure sector unless the manifold is rigid.

Core claim

In the DGKT scenario on a generic Calabi-Yau three-fold, a recently proposed holographic constraint on cubic couplings is satisfied if and only if the Calabi-Yau is rigid, i.e. when h^{2,1}=0. More generally, in 4d N=1 supergravity extremal cubic couplings are determined by the third derivatives of the real, Kähler-invariant superpotential, while the eigenvalues of its Hessian compute the conformal dimensions of the dual scalar operators. Applying them to supersymmetric DGKT vacua, extremal cubic couplings always vanish in the Kähler + universal CS/dilaton sector, whereas non-vanishing (super-)extremal couplings are always present in the complex structure sector.

What carries the argument

The third derivatives of the real Kähler-invariant superpotential, which fix the extremal cubic couplings, together with the holographic constraint that requires these couplings to obey specific bounds.

If this is right

Non-rigid Calabi-Yau threefolds with h^{2,1} > 0 introduce non-vanishing cubic couplings in the complex structure sector that violate the holographic constraint.
The Kähler plus universal sector of DGKT vacua always produces vanishing extremal cubic couplings independently of the threefold.
The conformal dimensions of the dual scalar operators are read off from the eigenvalues of the Hessian of the Kähler-invariant superpotential.
Only rigid threefolds allow consistent DGKT vacua under the stated holographic constraint.

Where Pith is reading between the lines

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

Similar holographic constraints may select rigid geometries in other classes of flux vacua beyond DGKT.
Explicit spectra calculations on known rigid Calabi-Yau examples would provide a direct numerical check of the vanishing statements.
The result raises the question whether rigidity remains necessary when supersymmetry is broken.

Load-bearing premise

The holographic constraint on cubic couplings is taken to apply directly to the supersymmetric DGKT vacua with the Kähler and complex structure sectors remaining decoupled enough for independent vanishing statements.

What would settle it

An explicit computation on a Calabi-Yau threefold with h^{2,1} greater than zero that produces vanishing cubic couplings in the complex structure sector would falsify the if-and-only-if statement.

read the original abstract

We show that in the DGKT scenario on a generic Calabi-Yau three-fold, a recently proposed holographic constraint on cubic couplings is satisfied if and only if the Calabi-Yau is rigid, i.e. when $h^{2,1}=0$. More generally, we illustrate how in 4d $\mathcal{N}=1$ supergravity, extremal cubic couplings are determined by the third derivatives of the real, K\"ahler-invariant superpotential, while the eigenvalues of its Hessian compute the conformal dimensions of the dual scalar operators. These results extend more broadly beyond 4d $\mathcal{N}=1$ supergravity. Applying them to supersymmetric DGKT vacua, we prove that extremal cubic couplings always vanish in the K\"ahler + universal CS/dilaton sector, whereas non-vanishing (super-)extremal couplings are always present in the complex structure sector. It follows that the holographic constraint is satisfied in DGKT if and only if the Calabi-Yau three-fold is rigid with $h^{2,1}=0$.

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.

Desk Editor's Note private letter to a colleague

DGKT satisfies the holographic cubic constraint iff the CY3 is rigid, because the Kähler-invariant superpotential derivatives vanish in one sector but not the other.

read the letter

The paper shows that in DGKT flux vacua on a Calabi-Yau threefold the holographic constraint on cubic couplings holds exactly when h^{2,1}=0. It reaches this by first deriving, in general 4d N=1 supergravity, that extremal cubic couplings come from the third derivatives of the real Kähler-invariant superpotential and that the Hessian eigenvalues give the dual operator dimensions. These relations are stated cleanly and look reusable.

They then apply the same formulae to the DGKT superpotential. The key step is proving that the couplings vanish identically in the Kähler plus universal CS/dilaton sector while remaining non-vanishing in the complex-structure sector whenever h^{2,1}>0. The iff statement follows at once.

The general N=1 expressions are the most useful part; they organize the data without extra assumptions. The DGKT application is direct and the sector separation is asserted after the projection to the real Kähler-invariant quantity.

The stress-test worry about cross terms from the axio-dilaton mixing in W does not appear to survive the projection, since the paper states an explicit proof that the vanishing holds in one sector and the non-vanishing in the other. No obvious internal contradiction shows up in the abstract or the claimed logic.

The result is narrow but concrete: it limits which geometries can host supersymmetric DGKT solutions that also satisfy the holographic condition. People working on flux vacua, DGKT constructions, or holographic constraints in string theory would get value from it. It is worth sending to referees because the derivation is self-contained and the conclusion is falsifiable within the stated framework.

Referee Report

1 major / 1 minor

Summary. The manuscript claims that in the DGKT scenario on a generic Calabi-Yau threefold, a recently proposed holographic constraint on cubic couplings is satisfied if and only if the Calabi-Yau is rigid (h^{2,1}=0). It first derives general results in 4d N=1 supergravity: extremal cubic couplings are determined by third derivatives of the real Kähler-invariant superpotential, while eigenvalues of its Hessian give conformal dimensions of dual scalar operators. These are then applied to supersymmetric DGKT vacua (with superpotential W=∫(F−ϕH)∧Ω) to prove that extremal cubic couplings vanish identically in the Kähler + universal CS/dilaton sector but are non-vanishing in the complex-structure sector whenever h^{2,1}>0, yielding the stated iff condition on rigidity.

Significance. If the central claims hold, the work establishes a direct geometric criterion linking Calabi-Yau rigidity to the satisfaction of a holographic constraint in DGKT flux vacua, using general N=1 SUGRA properties of the Kähler-invariant superpotential. The general formulae for cubic couplings and Hessian spectra are potentially reusable in other N=1 settings. The iff statement is a sharp, testable prediction that could sharpen discussions of the string landscape and AdS/CFT consistency conditions in flux compactifications.

major comments (1)

[DGKT vacua analysis] DGKT vacua analysis: the iff conclusion rests on the claim that extremal cubic couplings (third derivatives of the real Kähler-invariant superpotential) vanish in the Kähler + universal CS/dilaton sector while remaining non-vanishing in the CS sector for h^{2,1}>0. Because W=∫(F−ϕH)∧Ω mixes the axio-dilaton ϕ with the complex-structure periods inside Ω, an explicit computation is required to confirm that the real Kähler-invariant projection eliminates all cross-sector contributions to these third derivatives; without it the independent vanishing/non-vanishing statements used to link the holographic constraint to rigidity are not yet verified.

minor comments (1)

[Abstract] The abstract refers to a 'recently proposed holographic constraint' without a citation; adding the reference would help readers locate the precise statement being tested.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment on the DGKT analysis. We address the point below.

read point-by-point responses

Referee: DGKT vacua analysis: the iff conclusion rests on the claim that extremal cubic couplings (third derivatives of the real Kähler-invariant superpotential) vanish in the Kähler + universal CS/dilaton sector while remaining non-vanishing in the CS sector for h^{2,1}>0. Because W=∫(F−ϕH)∧Ω mixes the axio-dilaton ϕ with the complex-structure periods inside Ω, an explicit computation is required to confirm that the real Kähler-invariant projection eliminates all cross-sector contributions to these third derivatives; without it the independent vanishing/non-vanishing statements used to link the holographic constraint to rigidity are not yet verified.

Authors: We agree that an explicit verification of the decoupling under the real Kähler-invariant projection would strengthen the presentation, given the mixing in W. The manuscript derives the general cubic-coupling formulae from the third derivatives without assuming a priori sector separation, and then applies the specific DGKT superpotential and Kähler potential to establish the vanishing in the Kähler+universal sector. However, to make the elimination of cross terms fully transparent, we will add an explicit component-wise computation of the relevant third derivatives (showing that mixed Kähler-CS contributions to the real projection vanish identically due to the structure of the periods and the real projection) in a new appendix. This will not alter the conclusions but will address the verification concern directly. revision: yes

Circularity Check

0 steps flagged

Minor self-citation on holographic constraint; central iff follows from superpotential derivative properties without reduction

full rationale

The paper states general N=1 formulae for extremal cubic couplings as third derivatives of the real Kähler-invariant superpotential and applies them to the DGKT superpotential W=∫(F−ϕH)∧Ω to prove vanishing in the Kähler+universal sector and non-vanishing in the complex-structure sector when h^{2,1}>0. The holographic constraint is invoked as an external recently-proposed condition whose satisfaction then yields the rigidity iff statement. No quoted step reduces a prediction to a fit, renames a known result, or makes the central claim depend on a self-citation chain that itself lacks independent verification. Sector separation is asserted after deriving the general formulae, and the derivation remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper builds on standard assumptions of 4d N=1 supergravity and the DGKT construction; no new free parameters or invented entities are indicated in the abstract.

axioms (2)

domain assumption Extremal cubic couplings in 4d N=1 supergravity are determined by the third derivatives of the real Kähler-invariant superpotential.
Stated as a general result extending beyond DGKT.
domain assumption DGKT vacua are supersymmetric AdS4 solutions obtained from type IIA compactifications on Calabi-Yau threefolds with fluxes.
Standard background for the specific application.

pith-pipeline@v0.9.1-grok · 5720 in / 1408 out tokens · 43876 ms · 2026-07-02T09:27:34.672369+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 14 internal anchors

[1]

Polchinski and E

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

work page doi:10.1142/9789814412551 2009
[2]

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

work page arXiv 2019
[3]

T. C. Collins, D. Jafferis, C. Vafa, K. Xu and S.-T. Yau,On Upper Bounds in Dimension Gaps of CFT’s,2201.03660

work page arXiv
[4]

Type IIA Moduli Stabilization

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor,Type IIA moduli stabilization,JHEP 07(2005) 066 [hep-th/0505160]

work page internal anchor Pith review Pith/arXiv arXiv 2005
[5]

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
[6]

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
[7]

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
[8]

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
[9]

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
[10]

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
[11]

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
[12]

Emergent Spacetime and Holographic CFTs

S. El-Showk and K. Papadodimas,Emergent Spacetime and Holographic CFTs,JHEP10 (2012) 106 [1101.4163]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[13]

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
[14]

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
[15]

Holography from Conformal Field Theory

I. Heemskerk, J. Penedones, J. Polchinski and J. Sully,Holography from Conformal Field Theory,JHEP10(2009) 079 [0907.0151]. 17

work page internal anchor Pith review Pith/arXiv arXiv 2009
[16]

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
[17]

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

work page arXiv 2020
[18]

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
[19]

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
[20]

S. M. Chester, R. Mouland, J. van Muiden and C. Virally,Extremal couplings and gluon scattering in M-theory,2512.04057

work page arXiv
[21]

Castro and P

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

work page arXiv 2024
[22]

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
[23]

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
[24]

Van Hemelryck,Supersymmetric scale-separated AdS 3 orientifold vacua of type IIB, JHEP10(2025) 109 [2502.04791]

V. Van Hemelryck,Supersymmetric scale-separated AdS 3 orientifold vacua of type IIB, JHEP10(2025) 109 [2502.04791]

work page arXiv 2025
[25]

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

work page arXiv 2022
[26]

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
[27]

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
[28]

Quirant,Noninteger conformal dimensions for type IIA flux vacua,Phys

J. Quirant,Noninteger conformal dimensions for type IIA flux vacua,Phys. Rev. D106 (2022) 066017 [2204.00014]

work page arXiv 2022
[29]

Ning,Holographic perspectives on models of moduli stabilization in M-theory,JHEP09 (2022) 042 [2206.13332]

S. Ning,Holographic perspectives on models of moduli stabilization in M-theory,JHEP09 (2022) 042 [2206.13332]

work page arXiv 2022
[30]

Plauschinn,Mass spectrum of type IIB flux compactifications — comments on AdS vacua and conformal dimensions,JHEP02(2023) 257 [2210.04528]

E. Plauschinn,Mass spectrum of type IIB flux compactifications — comments on AdS vacua and conformal dimensions,JHEP02(2023) 257 [2210.04528]

work page arXiv 2023
[31]

Andriot and G

D. Andriot and G. Tringas,Extensions of a scale-separated AdS 4 solution and their mass spectrum,JHEP01(2024) 008 [2310.06115]

work page arXiv 2024
[32]

Arboleya, A

´A. Arboleya, A. Guarino and M. Morittu,On type IIB AdS 3 flux vacua with scale separation and integer conformal dimensions,PoSCORFU2024(2025) 184 [2504.21508]

work page arXiv 2025
[33]

Arboleya, G

´A. Arboleya, G. Casagrande, A. Guarino and M. Morittu,Taxonomy of type II orientifold flux vacua in 3D,2512.13433

work page arXiv
[34]

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. 18

work page internal anchor Pith review Pith/arXiv arXiv
[35]

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
[36]

A note on the holographic consistency of DGKT-type vacua with $h^{2,1}=0$

F. Revello and F. Verbeure,A note on the holographic consistency of DGKT-type vacua withh 2,1 = 0,2606.30341

work page internal anchor Pith review Pith/arXiv arXiv
[37]

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
[38]

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
[39]

Bobev and H

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

work page arXiv 2025
[40]

Massive IIA flux compactifications and U-dualities

T. Banks and K. van den Broek,Massive IIA flux compactifications and U-dualities, JHEP03(2007) 068 [hep-th/0611185]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[41]

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
[42]

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
[43]

Van Hemelryck,Scale-Separated AdS3 Vacua from G2-Orientifolds Using Bispinors, Fortsch

V. Van Hemelryck,Scale-Separated AdS3 Vacua from G2-Orientifolds Using Bispinors, Fortsch. Phys.70(2022) 2200128 [2207.14311]

work page arXiv 2022
[44]

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]

work page internal anchor Pith review Pith/arXiv arXiv 2021
[45]

Shift Symmetries in (Anti) de Sitter Space

J. Bonifacio, K. Hinterbichler, A. Joyce and R. A. Rosen,Shift Symmetries in (Anti) de Sitter Space,JHEP02(2019) 178 [1812.08167]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[46]

Apers,Aspects of AdS flux vacua with integer conformal dimensions,JHEP05(2023) 040 [2211.04187]

F. Apers,Aspects of AdS flux vacua with integer conformal dimensions,JHEP05(2023) 040 [2211.04187]

work page arXiv 2023
[47]

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
[48]

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
[49]

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

work page arXiv
[50]

Apers, M

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

work page arXiv 2026
[51]

Bedroya and P

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

work page arXiv
[52]

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

F. Apers,On the DGKT brane dual and its decoupling,2601.15093. 19

work page arXiv

[1] [1]

Polchinski and E

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

work page doi:10.1142/9789814412551 2009

[2] [2]

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

work page arXiv 2019

[3] [3]

T. C. Collins, D. Jafferis, C. Vafa, K. Xu and S.-T. Yau,On Upper Bounds in Dimension Gaps of CFT’s,2201.03660

work page arXiv

[4] [4]

Type IIA Moduli Stabilization

O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor,Type IIA moduli stabilization,JHEP 07(2005) 066 [hep-th/0505160]

work page internal anchor Pith review Pith/arXiv arXiv 2005

[5] [5]

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

[6] [6]

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

[7] [7]

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

[8] [8]

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

[9] [9]

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

[10] [10]

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

[11] [11]

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

[12] [12]

Emergent Spacetime and Holographic CFTs

S. El-Showk and K. Papadodimas,Emergent Spacetime and Holographic CFTs,JHEP10 (2012) 106 [1101.4163]

work page internal anchor Pith review Pith/arXiv arXiv 2012

[13] [13]

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

[14] [14]

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

[15] [15]

Holography from Conformal Field Theory

I. Heemskerk, J. Penedones, J. Polchinski and J. Sully,Holography from Conformal Field Theory,JHEP10(2009) 079 [0907.0151]. 17

work page internal anchor Pith review Pith/arXiv arXiv 2009

[16] [16]

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

[17] [17]

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

work page arXiv 2020

[18] [18]

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

[19] [19]

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

[20] [20]

S. M. Chester, R. Mouland, J. van Muiden and C. Virally,Extremal couplings and gluon scattering in M-theory,2512.04057

work page arXiv

[21] [21]

Castro and P

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

work page arXiv 2024

[22] [22]

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

[23] [23]

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

[24] [24]

Van Hemelryck,Supersymmetric scale-separated AdS 3 orientifold vacua of type IIB, JHEP10(2025) 109 [2502.04791]

V. Van Hemelryck,Supersymmetric scale-separated AdS 3 orientifold vacua of type IIB, JHEP10(2025) 109 [2502.04791]

work page arXiv 2025

[25] [25]

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

work page arXiv 2022

[26] [26]

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

[27] [27]

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

[28] [28]

Quirant,Noninteger conformal dimensions for type IIA flux vacua,Phys

J. Quirant,Noninteger conformal dimensions for type IIA flux vacua,Phys. Rev. D106 (2022) 066017 [2204.00014]

work page arXiv 2022

[29] [29]

Ning,Holographic perspectives on models of moduli stabilization in M-theory,JHEP09 (2022) 042 [2206.13332]

S. Ning,Holographic perspectives on models of moduli stabilization in M-theory,JHEP09 (2022) 042 [2206.13332]

work page arXiv 2022

[30] [30]

Plauschinn,Mass spectrum of type IIB flux compactifications — comments on AdS vacua and conformal dimensions,JHEP02(2023) 257 [2210.04528]

E. Plauschinn,Mass spectrum of type IIB flux compactifications — comments on AdS vacua and conformal dimensions,JHEP02(2023) 257 [2210.04528]

work page arXiv 2023

[31] [31]

Andriot and G

D. Andriot and G. Tringas,Extensions of a scale-separated AdS 4 solution and their mass spectrum,JHEP01(2024) 008 [2310.06115]

work page arXiv 2024

[32] [32]

Arboleya, A

´A. Arboleya, A. Guarino and M. Morittu,On type IIB AdS 3 flux vacua with scale separation and integer conformal dimensions,PoSCORFU2024(2025) 184 [2504.21508]

work page arXiv 2025

[33] [33]

Arboleya, G

´A. Arboleya, G. Casagrande, A. Guarino and M. Morittu,Taxonomy of type II orientifold flux vacua in 3D,2512.13433

work page arXiv

[34] [34]

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. 18

work page internal anchor Pith review Pith/arXiv arXiv

[35] [35]

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

[36] [36]

A note on the holographic consistency of DGKT-type vacua with $h^{2,1}=0$

F. Revello and F. Verbeure,A note on the holographic consistency of DGKT-type vacua withh 2,1 = 0,2606.30341

work page internal anchor Pith review Pith/arXiv arXiv

[37] [37]

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

[38] [38]

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

[39] [39]

Bobev and H

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

work page arXiv 2025

[40] [40]

Massive IIA flux compactifications and U-dualities

T. Banks and K. van den Broek,Massive IIA flux compactifications and U-dualities, JHEP03(2007) 068 [hep-th/0611185]

work page internal anchor Pith review Pith/arXiv arXiv 2007

[41] [41]

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

[42] [42]

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

[43] [43]

Van Hemelryck,Scale-Separated AdS3 Vacua from G2-Orientifolds Using Bispinors, Fortsch

V. Van Hemelryck,Scale-Separated AdS3 Vacua from G2-Orientifolds Using Bispinors, Fortsch. Phys.70(2022) 2200128 [2207.14311]

work page arXiv 2022

[44] [44]

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]

work page internal anchor Pith review Pith/arXiv arXiv 2021

[45] [45]

Shift Symmetries in (Anti) de Sitter Space

J. Bonifacio, K. Hinterbichler, A. Joyce and R. A. Rosen,Shift Symmetries in (Anti) de Sitter Space,JHEP02(2019) 178 [1812.08167]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[46] [46]

Apers,Aspects of AdS flux vacua with integer conformal dimensions,JHEP05(2023) 040 [2211.04187]

F. Apers,Aspects of AdS flux vacua with integer conformal dimensions,JHEP05(2023) 040 [2211.04187]

work page arXiv 2023

[47] [47]

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

[48] [48]

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

[49] [49]

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

work page arXiv

[50] [50]

Apers, M

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

work page arXiv 2026

[51] [51]

Bedroya and P

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

work page arXiv

[52] [52]

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

F. Apers,On the DGKT brane dual and its decoupling,2601.15093. 19

work page arXiv