Supersymmetric AdS(4) compactifications of IIA supergravity

D. Lust; D. Tsimpis

REVIEW

Supersymmetric AdS(4) compactifications of IIA supergravity

D. Lust, D. Tsimpis

High Energy Physics - Theory · Submitted 21 Dec 2004 · 51 references

Pith's verdict: A clean and quotable classification of half-flat N=1 AdS4 vacua in massive IIA, but the 'sufficient' half of the title rests on an integrability step the paper asserts rather than shows for B'≠0.

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arXiv IDhep-th/0412250 (version 2)

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CitationD. Lust, D. Tsimpis. "Supersymmetric AdS(4) compactifications of IIA supergravity." arXiv:hep-th/0412250 (2004). https://pith.science/paper/Q44BBLRY

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The durable contribution here is the torsion-class result, not the 'necessary and sufficient' framing. Lüst and Tsimpis reduce the N=1 AdS4 conditions for massive IIA to a compact set of equations — (4.19), (4.24), (4.29) — with W1+=W2+=W3=W4=W5=0, W1- and W2- nonzero, and dW2- ∝ Re Ω. That is a clean, citable statement, and it correctly recovers the Behrndt-Cvetic nearly-Kähler case at f² = (108m²/5)e^{2φ}. The massless limit lifting to M-theory on a twisted circle over a half-flat base is a nice bonus. The case analysis on |α| versus |β| is careful, and the tensor decomposition in Section 3.2 is done properly. They are also honest that both worked examples — T² over K3 and the Iwasawa manifold — satisfy the torsion conditions but miss the proportionality constant in (4.25). That honesty counts in their favor, but it also means the solution class has no known compact representative yet; it could be empty. That is the practical weakness, and they say so themselves, so I won't belabor it. The real soft spot is sufficiency. Section 2 sets B'=0 'for simplicity of presentation' and asserts the conclusion survives a nonzero B'. The massive case is precisely the paper's new content, and the B' terms enter both the supercovariant derivative (2.16) and the dilatino variation (2.15). They explicitly check the dilaton equation for the solution but conspicuously do not say the same for Einstein. So the 'sufficient' in the abstract is not fully earned for m≠0. It is probably fixable — the structure suggests the quadratic B' pieces of (2.9) do assemble from the [D,D] commutator — but it is not shown. On the reader's E_{0M}=0 worry: that proviso is fine for the warped-product ansatz, the mixed components vanish trivially, so it is not the gap. The stress-test has the right target. One more thing a referee should press on: the claim in 4.4 that no nearly-Kähler M-theory AdS4 solutions exist, contra Lukas-Saffin, is sharp and deserves a careful look. Send it out. It is a solid classification paper in a crowded subfield and will be cited by anyone working on half-flat IIA vacua.

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Major objections (2)

[§2, integrability argument] The sufficiency direction of the abstract's 'necessary and sufficient' claim is established only for B'=0. The text states 'For the purposes of this subsection we set B'=0 for simplicity of presentation. The conclusion does not change by introducing a nonzero B'-field,' but this is asserted, not shown. Since the massive case (m≠0, B'≠0) is the paper's main new result, and since the B' terms enter both the supercovariant derivative (2.16) and the dilatino variation (2.15), the reader cannot verify that they combine into the B'-dependent pieces of the Einstein equation (2.9) and dilaton equation (2.10) under the [D,D] and dilatino-square manipulations. The paper explicitly checks the dilaton equation for the solution (4.19) but does not say the same for the Einstein equation. Either extend the Section 2 argument to B'≠0 or verify (2.9) explicitly for (4.19); otherwise the 'sufficient' half of the headline claim is not established for the massive case.
[Abstract (s1) and §5] The paper announces 'new solutions' but no explicit compact example satisfying all conditions—in particular the proportionality constant in (4.25)—is exhibited. The authors acknowledge this in the introduction and in §5.1 ('there are no values of f, m, other than f=m=0, that can fit with the above equation'), and the two worked examples satisfy (1.1,1.2) but not (4.25). This is an honest limitation, but the abstract's unqualified 'we find new solutions' overstates what is established. Either qualify the abstract (e.g., 'we derive the conditions and exhibit candidate geometries') or provide at least one example satisfying (4.25).

Minor objections (7)

[Introduction vs. §5.2] The introduction says that for the Iwasawa example of [21] 'the intrinsic torsion is entirely contained in W3,' whereas §5.2 finds an SU(3) structure on the Iwasawa manifold with torsion in W1- ⊕ W2-. These are presumably different SU(3) structures on the same underlying manifold; please state this explicitly to avoid the appearance of a contradiction.
[Eqs. (4.19) and (4.31)] The coefficient of the J-term in mB is 1/8 in (4.19), but taking the massless limit via the Stückelberg relation (2.6) gives F = (1/4)fe^{-φ/2}J + F̃, whereas (4.31) has 1/9. Since (4.31) is self-consistent with the Bianchi identity (4.32), the coefficient in (4.19) is presumably 1/18; please check.
[Eqs. (3.20)-(3.21)] With J_{mn}J^{np} = -δ_m^p (3.15), the trace part as written gives B(0) = B_{mn}J^{mn} = -B(0). Please check the sign (and the corresponding normalization in (4.19)).
[Eq. (4.28)] As written, setting m=0 gives f=0, which appears to contradict the massless solution (4.31) with f≠0. The resolution is that the limit must be taken with mB̃ held fixed (so m²|B̃|² → |F̃|²/4); this should be stated explicitly, since the sentence 'The massless limit should be taken with care' is easy to miss.
[Abstract (s2)] 'All fluxes are given in terms of the geometrical data' is slightly overstated. Eq. (4.25) determines dB̃ in terms of the geometry and (4.26) requires d*B̃=0, so B̃ is fixed only up to harmonic primitive (1,1) forms; the same applies to F̃ in the massless case. Please qualify.
[§4.1 and §4.2] The passage from (3.7)-(3.10) and (4.10) to (4.11)-(4.12), and the check that the form equations (2.11)-(2.12) are satisfied, are presented as results of 'solving' or 'using (B.13)' without intermediate steps. Given that these are the technical core of the paper, a few more lines of detail (or an appendix) would help the reader verify them.
[Abstract and §3.1] The 'necessary' direction is established within the warped-product ansatz (3.1)-(3.4), which assumes an AdS4 factor and specific form components. The abstract should say 'within the warped-product ansatz' to avoid overclaiming.

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The paper

The paper claims

The paper derives necessary and sufficient conditions for N=1 compactifications of massive type IIA supergravity to four-dimensional anti-de Sitter space, and shows that every flux is then fixed by the geometry of the internal six-manifold.

The reading

Type IIA string theory can be compactified to four dimensions with fluxes — background values for the antisymmetric form fields — turned on. The question this paper takes up is what the internal six-dimensional geometry must be for such a compactification to preserve N=1 supersymmetry and land on anti-de Sitter space rather than flat Minkowski space. Working in the language of SU(3) structures, the authors derive conditions claimed to be both necessary and sufficient, and find a new family of solutions with constant dilaton and every form field switched on. The payoff is that the fluxes are not free parameters: they are read off from the torsion of the internal manifold, which is constrained to a special half-flat class.

What carries the argument

The engine is the SU(3)-structure decomposition. A single globally defined spinor $η$ on $X_6$ defines a real two-form $J$ and a complex three-form $Ω$, and the failure of these to be closed is packaged into five torsion classes $W_1$ through $W_5$ appearing in $dJ$ and $dΩ$. Every form field is expanded into irreducible SU(3) pieces (a scalar, a vector, an eight, a six, and so on), and the supersymmetry variations are then contracted with gamma matrices to project out each representation one at a time. This turns ten-dimensional Killing-spinor equations into algebraic relations among a handful of numbers, which is what makes the classification tractable.

Extended reading notes

Core claim

The central claim is that N=1 supersymmetric compactifications of (massive) type IIA supergravity to $AdS_4$ are completely characterized by a short list of conditions. The ten-dimensional fields take the form $mB = (f/18)e^{-φ/2}J + m B̃$, $H = (4m/5)e^{7φ/4}Re(Ω)$, and $G = f dVol_4 + (3m/5)e^{φ}J ∧ J$, with constant dilaton, constant warp factor up to a fixed power of $e^{-φ}$, and $B̃$ a primitive two-form. The internal manifold $X_6$ must carry an SU(3) structure whose intrinsic torsion lies entirely in the two classes $W_1^-$ and $W_2^-$, with all other torsion classes vanishing, so $X_6$ is half-flat. An extra condition inherited from the Bianchi identity, $d B̃ ∝ Re(Ω)$, fixes the proportionality constant in terms of the mass and the flux parameter $f$, and forces $f^2 ≥ (108m^2/5)e^{2φ}$. The authors argue that once supersymmetry, the Bianchi identities and the form-field equations are imposed, the dilaton and Einstein equations follow automatically, so no further constraints are needed.

Load-bearing premise

The claim that supersymmetry plus the Bianchi identities plus the form-field equations automatically imply the dilaton and Einstein equations rests on an unproven condition, stated in Section 2 and asserted to hold for the compactifications at hand, that the mixed time-space components of the Einstein tensor vanish.

Editorial extensions

If this is right

Every flux in the vacuum — the mass parameter, the NS two-form, the RR two- and four-forms — is determined by the torsion data of the internal manifold rather than chosen by hand.
The internal space is restricted to half-flat manifolds with torsion in $W_1^- ⊕ W_2^-$, a narrower class than the half-flat manifolds allowed by supersymmetry alone.
In the limit $f^2 = (108m^2/5)e^{2φ}$ the primitive part of the two-form vanishes, all torsion except $W_1^-$ disappears, and the construction collapses to the previously known nearly-Kähler solutions.
In the massless limit the solution lifts to eleven dimensions as a twisted circle fibration over a half-flat six-manifold, expected to have a three-dimensional conformal field theory dual.
The results imply that no compactification of eleven-dimensional supergravity to $AdS_4$ on a product of a circle and a six-dimensional nearly-Kähler manifold exists, closing off a case left open in earlier work.

Reading between the lines

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

The paper's own two example families — $T^2$ fibrations over K3 and the Iwasawa manifold — satisfy the torsion conditions but miss the required constant in $d B̃ ∝ Re(Ω)$ by a fixed factor, so the authors do not actually exhibit a single fully working solution. Whether the class is nonempty is therefore the live question, not a detail.
If the class does turn out to be empty, the natural reading is that the Bianchi identity is doing more work than supersymmetry: it is the topology of $X_6$, not the Killing spinor equations, that decides which torsion classes are realizable.
Because the fluxes are algebraic in the torsion, one could imagine scanning known nilmanifolds and solvmanifolds systematically for the exact proportionality constant, rather than constructing examples one at a time.
The integrability argument that lets the authors drop the dilaton and Einstein equations is a template that would transfer to other flux backgrounds, so its validity is a claim of broader scope than the specific $AdS_4$ vacua derived here.

Original abstract

We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.

The compiled record

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,522 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures.	contribution 0.85	0.96	0.42	asserted 1.00
s1	We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields.	result 0.95	0.96	0.34	asserted 1.00
s2	All fluxes are given in terms of the geometrical data of the internal compact space.	result 0.98	0.88	0.17	asserted 1.00
s3	The latter is constrained to belong to a special class of half-flat manifolds.	result 0.98	0.78	0.19	asserted 1.00

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

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arXiv listing abstract v2

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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M-theory and Type IIA Flux Compactifications
hep-th 2012-08 conditional novelty 7.0 of 10

New higher-derivative M-theory couplings involving fluxes and curvatures generate M5-brane charge, evading the supergravity no-go theorem and permitting Minkowski flux compactifications of M-theory and type IIA.
N=2 supersymmetric AdS_4 solutions of M-theory
hep-th 2012-07 accept novelty 7.0 of 10

The most general N=2 supersymmetric AdS_4 backgrounds of M-theory are classified via a local SU(2)-structure, and a new warped AdS_4 x S^7 solution dual to a cubic deformation is found numerically.
The gauge dual of Romans mass
hep-th 2009-01 conditional novelty 7.0 of 10

The Romans mass F0 of massive IIA on AdS4 x CP3 equals the sum of the two Chern-Simons levels of the dual ABJM-like field theory.
Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold
hep-th 2005-06 conditional novelty 7.0 of 10

Adding RR, NS and metric fluxes to a T^6/(Omega(-1)^F_L I_3) Type IIA orientifold stabilizes all closed-string moduli in supersymmetric AdS vacua, and one such vacuum hosts a three-generation MSSM-like intersecting D6...
Generalized structures of N=1 vacua
hep-th 2005-05 conditional novelty 7.0 of 10

N=1 type II vacua with Ramond-Ramond flux are characterized by two pure spinor equations: one requires a twisted generalized Calabi-Yau, the other sources the second spinor with the RR field.
Scale-separated AdS$_4$ vacua of IIA orientifolds and M-theory
hep-th 2021-06 conditional novelty 6.0 of 10

Massless IIA admits scale-separated AdS4 flux vacua whose orientifold backreaction is perturbatively small, and the strongly coupled ones lift to singular but scale-separated 11D geometries.
On supersymmetric AdS$_4$ orientifold vacua
hep-th 2020-03 conditional novelty 6.0 of 10

An explicit first-order-in-coupling ten-dimensional type IIA background with localized O6-planes is constructed whose supersymmetry equations and Bianchi identities are solved, matching the DGKT AdS4 flux vacuum at le...
A Landscape of AdS Flux Vacua
hep-th 2019-08 conditional novelty 6.0 of 10

A bilinear flux-axion polynomial technique yields new branches of type IIA Calabi-Yau flux vacua, including a tachyon-free non-supersymmetric AdS branch.
Supersymmetry and non-Abelian T-duality in type II supergravity
hep-th 2014-09 accept novelty 6.0 of 10

Supersymmetry preservation under Abelian and SU(2) non-Abelian T-duality is governed by the Kosmann spinorial Lie derivative, which vanishes exactly when the original Killing spinors are independent of the T-duality d...
AdS_6 solutions of type II supergravity
hep-th 2014-06 conditional novelty 6.0 of 10

Every supersymmetric AdS_6 x M_4 solution of type IIB supergravity has an internal space that is an S^2 fibration over a two-dimensional base, with the metric and fluxes fixed by two PDEs.
A note on obstinate tachyons in classical dS solutions
hep-th 2012-12 conditional novelty 6.0 of 10

In massive IIA flux compactifications on SU(3)-structure manifolds, every known de Sitter critical point has its tachyon inside the subspace spanned by the dilaton, the total volume, and the orientifold-cycle volumes.
All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua
hep-th 2012-08 accept novelty 6.0 of 10

Eleven-dimensional supergravity on any seven-dimensional SU(3)-structure manifold reduces to four-dimensional N=2 gauged supergravity with vector-multiplet, Heisenberg-algebra, and hyperscalar isometries, and the fram...
Supersymmetric AdS vacua and separation of scales
hep-th 2012-06 conditional novelty 6.0 of 10

In massive IIA AdS4 x S2(B4) vacua the geometric moduli are independent and survive flux quantization, but the equations force the AdS and internal sizes to coincide near the middle of the internal space, so no scale ...
Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
hep-th 2011-05 conditional novelty 6.0 of 10

Reducing M-theory on a circle yields Chern-Simons quiver gauge theories dual to AdS4 x Y^{p,q}(CP2) for the full range of q and for every torsion G4 flux, with ranks and levels that differ from the earlier equal-rank ...
De Sitter hunting in a classical landscape
hep-th 2011-03 accept novelty 6.0 of 10

A systematic scan of homogeneous SU(3)-structure compactifications finds many classical de Sitter critical points, but all are perturbatively unstable and the explicit SU(2)xSU(2) example fails flux quantization in th...
Moduli Stabilization and Cosmology of Type IIB on SU(2)-Structure Orientifolds
hep-th 2009-12 accept novelty 6.0 of 10

Flux compactifications of type IIB on SU(2)-structure orientifolds stabilize all moduli in AdS but are ruled out for de Sitter vacua and slow-roll inflation by new no-go theorems in all but one model, which itself giv...
Towards Classical de Sitter Solutions in String Theory
hep-th 2009-07 accept novelty 6.0 of 10

Type IIA O6 compactifications on SU(3)-structure manifolds admit de Sitter solutions only if the torsion classes satisfy two conditions that no known coset or nilmanifold meets, though the same analysis yields new non...
Generalized non-supersymmetric flux vacua
hep-th 2008-07 conditional novelty 6.0 of 10

A classification of non-supersymmetric type II flux vacua by which D-branes remain BPS, yielding no-scale Minkowski examples and new AdS4 solutions.
Simple de Sitter Solutions
hep-th 2007-12 conditional novelty 6.0 of 10

A type IIA compactification on two nilmanifolds with orientifolds, KK5-branes, and fluxes yields metastable de Sitter minima whose curvature, coupling, and Hubble scale can be tuned small.
From ten to four and back again: how to generalize the geometry
hep-th 2007-07 conditional novelty 6.0 of 10

The ten-dimensional supersymmetry equations of warped SU(3)xSU(3) flux vacua are exactly the F- and D-flatness conditions of a Weyl-invariant four-dimensional N=1 supergravity, and non-perturbative corrections deform ...
Supersymmetric sources, integrability and generalized-structure compactifications
hep-th 2007-06 conditional novelty 6.0 of 10

Orientifolds are compatible with dynamic SU(3)xSU(3)-structure, and source-corrected Einstein and dilaton equations follow from supersymmetry plus form Bianchi identities.
A scan for new N=1 vacua on twisted tori
hep-th 2006-09 conditional novelty 6.0 of 10

The paper classifies N=1 Minkowski vacua of type II strings on compact nilmanifolds and solvmanifolds, finding a few new non-Calabi-Yau backgrounds that so far exist only as smeared large-volume solutions.
Supersymmetric D-branes and calibrations on general N=1 backgrounds
hep-th 2005-07 conditional novelty 6.0 of 10

Supersymmetric D-branes in general N=1 flux backgrounds wrap generalized complex submanifolds and are calibrated by a form built from the non-integrable pure spinor plus the Ramond-Ramond potentials.
N=1 effective potential from dual type-IIA D6/O6 orientifolds with general fluxes
hep-th 2005-03 conditional novelty 6.0 of 10

A dual formulation of type-IIA string theory yields a geometric superpotential and a family of fluxes that stabilize all seven moduli in a supersymmetric AdS4 vacuum.
On the Cosmology of Type IIA Compactifications on SU(3)-structure Manifolds
hep-th 2008-12 accept novelty 5.5 of 10

A refined no-go theorem rules out de Sitter vacua and slow-roll inflation for six of seven SU(3)-structure coset compactifications of type IIA string theory, and the surviving SU(2)xSU(2) case yields only saddle point...
Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections
hep-th 2013-03 conditional novelty 5.0 of 10

Intersecting Q- and R-branes, obtained by T-duality from NS5-branes and KK-monopoles, yield supersymmetric AdS4 x M6 backgrounds whose internal tori carry non-geometric Q- and R-fluxes and exhibit non-commutative or n...
A note on supersymmetric AdS_6 solutions of massive type IIA supergravity
hep-th 2012-09 conditional novelty 5.0 of 10

A complete case analysis of the supersymmetry conditions shows that the warped AdS_6 x S^4 solution of Brandhuber and Oz is the unique SO(5,2)-invariant supersymmetric AdS_6 background of massive type IIA supergravity.
The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets
hep-th 2008-06 conditional novelty 5.0 of 10

Explicit four-dimensional effective theories for type IIA AdS4 compactifications on nilmanifolds and cosets show all moduli stabilized in all but one coset model, with a Kaluza-Klein cross-check confirming the mass spectra.
Fixing Moduli in Exact Type IIA Flux Vacua
hep-th 2006-07 conditional novelty 5.0 of 10

Type IIA flux vacua with O6-planes have a half-flat, non-Calabi-Yau internal geometry; when the O6 charge is smeared, an exact Calabi-Yau solution exists and reproduces the known four-dimensional moduli stabilization.
Flux compactifications in string theory: a comprehensive review
hep-th 2005-09 accept novelty 3.0 of 10

A structured survey of type II flux compactifications: which fluxes preserve N=1, why compact spaces need orientifold planes, how fluxes generate superpotentials, and how far they go toward fixing moduli.
String Cosmology: from the Early Universe to Today
hep-th 2023-03 conditional novelty 2.0 of 10

A comprehensive survey that organizes moduli stabilisation, string inflation, post-inflationary moduli domination, dark energy, and alternative early-universe scenarios into a single reference with observational targets.
The Swampland: Introduction and Review
hep-th 2019-03 accept novelty 2.0 of 10

The review organizes the Swampland conjectures, from the Weak Gravity Conjecture to the de Sitter conjecture, and assesses the string-theory and black-hole evidence for each.

How later papers used it

101 later papers cite it

Evidence: substantial. 97 of the citing papers share no author with it, and 19 of those carry a confident label from Pith's citation classifier.

Pith read 19 of the 180 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 built on it and 1 used its method or tool. It appears under more than one label. 1 more paper by the same authors is listed: 1 built on it.

Builds on it 2 of 6 papers with this label · 1 by the same authors

Said it needed to understand how the solutions of this paper change in the presence of the O6.

Phenomenology from the Landscape of String Vacua (2008) · 0.98 · paraphrased: the licence does not allow quoting

By the same authors

Said that its ten-dimensional supergravity picture is contained in the class of solutions of this paper modified by the addition of smeared O6-planes.

AdS4 flux vacua in type II superstrings and their domain-wall solutions (2007) (same authors) · 0.94 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 paper

Used this paper's decomposition to obtain separate equations for every SU(3) representation in the decomposition of forms.

Phenomenology from the Landscape of String Vacua (2008) · 0.91 · paraphrased: the licence does not allow quoting

How the literature uses it

97 arXiv papers cite this in 175 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 117 sentences without a confident label

Contests it 1 paper

However, an $N=1$ supersymmetric $SU(3)$ structure solution requires a constant dilaton [ref] , and a constant dilaton is assumed in [ref] .

M-theory and Type IIA Flux Compactifications · Massive type IIA Supergravity · contest 0.81

Builds on it 5 papers

Since these vacua must also have O6-planes we need to understand how the solutions of [ref] change in the presence of the O6.

Phenomenology from the Landscape of String Vacua · IIA Supergravity with Orientifolds · 0.98
This corresponds to a consistent ten-dimensional supergravity picture: it is contained in the class of solutions of [ref] modified by the addition of smeared O6-planes.

AdS4 flux vacua in type II superstrings and their domain-wall solutions · Conclusions · 0.94
Below we generalise the AdS Ansatz of [ref] and check whether it can give rise to dS$_4$ solutions.

Towards Classical de Sitter Solutions in String Theory · O6 models on $(3)$-structure manifolds · 0.98

Uses its method or tool 1 paper

In this way, one obtains separate equations for every $SU(3)$ representation in the decomposition of forms [ref] : one can decompose the tensors $F$, $H$ and $G$ in terms of irreducible $SU(3)$ representations.

Phenomenology from the Landscape of String Vacua · Massive Type IIA Supergravity on $AdS_4$ · 0.91

Compares with it 6 papers

In some cases the solutions are mirror dual to the well known type IIA AdS flux vacua found by DeWolfe, Giryavets, Kachru and Taylor (DGKT) [ref] (see also [ref] for earlier work).

Type IIB flux compactifications with $h^{1,1}=0$ · Introduction · 0.95
It turns out that this condition leads to a particular set of SU(3)-structure manifolds, nearly-Kähler manifolds, which is a restricted set of solutions with respect to the class of supersymmetric SU(3)-structure backgrounds obtained in [ref] .

New families of scale separated vacua · 4d analysis · 0.99
The factor of $(-1)^s=±1$ arises in the following equations as unlike [ref] , we have fixed the phase of $Ω$ once and for all in ([ref]); see also [ref] .

Exploiting N=2 in consistent coset reductions of type IIA · The solution · 0.99

Cites it as support 5 papers

For constant dilaton and warp factor, it was shown in [ref] that, if only the singlets in the torsions are non-zero, no supersymmetric sourceless solutions exist.

N=1 SUSY AdS4 vacua in IIB SUGRA on group manifolds · Conclusion · 0.98
These configurations are forbidden [ref] because the Ramond-Ramond fluxes induce the non-zero valued NS-NS flux and some torsion classes.

AdS Vacua, Attractor Mechanism and Generalized Geometries · Search of (non)supersymmetric flux attractor vacua · 0.99
It is important to stress that all the supergravity equations of motion are satifsfied once the above supersymmetry conditions and the RR Bianchi identity ([ref]) are imposed [ref] .

On moduli and effective theory of N=1 warped flux compactifications · Pure spinors, $N=1$ conditions and generalized complex structure · 0.96

Cites it as background 31 papers

The general class of solutions was derived in [ref] , and later in the language of Generalized Geometry in [ref] .

N=1 SUSY AdS4 vacua in IIB SUGRA on group manifolds · T-duality of (0,0,25,-26,-23,24) · 0.85
The general form of the 10D supersymmetric solutions was found in [ref] (see also [ref] for earlier work).

Scale-separated AdS$_4$ vacua of IIA orientifolds and M-theory · Scale separation in IIA · 0.95
This supergravity theory has many (non)supersymmetric solutions of the form $AdS_4×M_6$ [ref] , where $M_6$ represents a six dimensional manifold.

${\cal N}=3$ Supersymmetric Effective Action of D2-branes in Massive IIA String Theory · Conclusion · 0.88

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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