Nongeometric Flux Compactifications

Brian Wecht; Jessie Shelton; Washington Taylor

REVIEW

Nongeometric Flux Compactifications

Jessie Shelton, Washington Taylor, Brian Wecht

High Energy Physics - Theory · Submitted 18 Aug 2005 · 45 references

Pith's verdict: A solid, well-known paper that organizes geometric and nongeometric NS-NS fluxes into one T-duality invariant superpotential; the Q-flux part is grounded, the R-flux part is formal and the authors say so.

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CitationBrian Wecht, Jessie Shelton, Washington Taylor. "Nongeometric Flux Compactifications." arXiv:hep-th/0508133 (2005). https://pith.science/paper/H4F5B4PL

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The thing to know: this is the paper that made nongeometric fluxes a systematic part of the flux compactification program, and the central construction holds up. The full superpotential (2.5)-(2.6) with all three P_i cubic, the flux table, and the T-duality rules (1.2) are the real content. The Q-flux terms come from explicit Buscher T-duality on known geometric results, and Section 3 writes down the T-fold metric and B-field (3.15)-(3.16), so you can see what a Q-flux background actually looks like. That part is on solid ground and is why people cite it. The constraint sets (4.2-4.8, 4.12-4.16) and the deformed gauge algebra (4.21-4.22) are useful well beyond the toroidal model, and the Jacobi-identity reading of the NS-NS constraints is a nice piece of organization. The R-flux is the soft spot, and the authors are upfront about it: Section 3 says they have no explicit presentation of an R-flux compactification, and Section 5 says the last T-duality must at this point be taken as a formal definition. The R terms in P3 are fixed by requiring T-duality invariance of W, which is then reported as a property of the result. That is a mild circularity, localized to R, and it is acknowledged. Read the R-flux claims as a motivated conjecture, not a derived background. On the stress-test concern about the IIA/IIB vacuum distributions: it is worth taking seriously but I do not think it lands as hard as stated. Since W and K are literally the same function of the same integers in both theories, the vacuum sets coincide iff the constraint lattices coincide. Section 4.2 asserts the IIA correspondence rather than deriving it term-by-term, and the same integer does denote different objects in the two frames (the check-c1 is Q on the IIB side, f on the IIA side). That is a genuine gap in exposition. But the framework is that the integers are the superpotential coefficients and the constraints are on those integers, so the claim holds at the level of the 4D effective theory provided the constraint derivation is right, which is plausible from T-duality but not proven exhaustive. The Delta-branch gap in Section 4.2 is minor; the stress-tester checked it and the branch is empty. One more thing: the detailed vacuum enumeration is deferred to [39], listed as to appear, so the headline claim about matching distributions is argued structurally here, not demonstrated by explicit counting. Who should read it: anyone working on flux compactifications, T-folds, or generalized geometry. It is a foundational reference. Recommendation: accept for peer review; serious paper, honest scope, clear writing.

Referee report

Major objections (2)

[Section 4.2, Eqs. (4.23)-(4.30)] The IIA counterpart of the constraint set is asserted rather than derived: the text says only 'In IIA these constraints come from, in order, (4.13), (4.15), and (the last two) (4.14).' This matters for [abstract:s3], because the claim that the IIA and IIB vacuum distributions coincide rests on the constraint lattices coinciding, and Table 1 shows that the same integer denotes different objects in the two frames (for example, the check-c1 is Q^{alpha j k} on the IIB side but f^{alpha j k} on the IIA side). A term-by-term derivation of at least one constraint, say (4.23), in the IIA frame, or a qualification of the abstract, would close the gap. I note that (4.17) is likely automatic in this model, since the Z2 x Z3 projection forces three-index objects to have one index per T^2, so the concern is mainly about (4.23)-(4.30).
[Section 4.2, the Delta-analysis] The text assumes both Delta_1 and Delta_2 are nonzero before concluding that both vanish, and the mixed branch (Delta_1 = 0, Delta_2 != 0) is not treated. I checked that branch and it is empty: it forces tilde-c1 = hat-c1 = check-c1 = c0 = c2 = 0 and then hat-c2^2 + hat-c2 check-c2 + check-c2^2 = 0, hence hat-c2 = check-c2 = 0. The conclusion therefore survives, but the claim that 'the full set of constraints is just (4.23)-(4.30) with hat-ci = check-ci' is not established as written; a sentence covering the mixed branch would fix it.

Minor objections (7)

[Table 1] The hat-c, check-c, tilde-c notation for the three Q-index positions is not explained in the table or its caption; a sentence would help the reader decode the entries.
[Eq. (2.6)] The overall factor 3U and the relative signs of the c-terms are not explained; the reader has to reverse-engineer them from Table 1.
[Section 2] The sentence 'This derivation relies only on duality transformations which can be performed explicitly ... and therefore is a rigorous demonstration' overstates the case: the U tau^2 and U tau^3 coefficients in IIB are obtained by the alpha <-> i exchange, which is a relabeling symmetry of the symmetric torus model, not a T-duality. The two steps should be distinguished.
[Section 4.2] 'One may show similarly that Qabc is antisymmetric under exchange of any upper and lower index, provided both indices are of the same kind' would benefit from a line of derivation.
[Abstract] 'The resulting structure is invariant under T-duality' is by construction in the R sector; 'invariant by construction' or a footnote pointing to Section 5 would be more precise.
[Section 2] The claim that there are no geometric W = 0 solutions in IIA uses the tadpole bound (4.9); this should be said explicitly.
[Reference [39]] The vacuum analysis is deferred to [39], listed as 'to appear'; the claims about the solution space are therefore partly conditional on that work.

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The paper

The paper claims

A T-duality invariant superpotential for type II torus compactifications is constructed that includes nongeometric Q and R fluxes alongside H-flux and geometric flux, making the IIA and IIB vacuum distributions identical.

The reading

String theory needs extra dimensions curled up small. The shape and size of those dimensions are governed by fields called moduli, and by fluxes, which are quantized amounts of field strength threading the compact space. Ordinary flux compactifications use H-flux (a 3-form) and geometric flux (a twist in how the torus is glued). A T-duality, a symmetry that swaps momentum and winding, turns H-flux into geometric flux, and a second T-duality turns geometric flux into a nongeometric flux called Q. This paper works out the full set of fluxes that can appear in the four-dimensional superpotential for a symmetric six-torus, including Q and a further formal object R obtained by a third T-duality. The result is a cubic polynomial in the complex structure modulus whose coefficients are all the quantized fluxes. Because the same superpotential appears in type IIA and type IIB, the two theories have the same set of supersymmetric vacua once nongeometric fluxes are allowed. The Q-flux is constructed explicitly as a T-fold: a space that is locally geometric but glued by a T-duality transformation. The R-flux is not constructed; it is inferred by requiring the superpotential to be T-duality invariant. The paper also derives the tadpole and Bianchi identity constraints that the fluxes must satisfy, and shows how the four-dimensional gauge algebra is deformed by the nongeometric fluxes.

Extended reading notes

Core claim

The full superpotential for the symmetric T^6 = (T^2)^3 orientifold model in both IIA and IIB is W = P1(tau) + S P2(tau) + U P3(tau) with all three P_i cubic in tau (Eqs. 2.5, 2.6), with coefficients given by integrally quantized H, f, Q and R fluxes as tabulated in Table 1. Because the superpotential and Kaehler potential (2.3) have the same form in both theories, the distributions of supersymmetric vacua in IIA and IIB are identical once nongeometric fluxes are included.

Load-bearing premise

The formal T-duality chain H -> f -> Q -> R (Eqs. 1.2, 5.1) defines a consistent flux coefficient even though the R-flux has no explicit geometric or T-fold construction. The authors state in Section 3 that 'we do not have an explicit presentation of a nongeometric compactification with such nongeometric fluxes' and in Section 5 that 'the last T-duality in (5.1) must at this point be taken as a formal definition.' The R-flux terms in P3 are fixed by requiring T-duality invariance of W, not derived from a background.

Original abstract

We investigate a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop T-duality rules for NS-NS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced four-dimensional theory. The resulting structure is invariant under T-duality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included. This gives a concrete framework in which to investigate the possibility that generic string compactifications may be nongeometric in any duality frame. The framework developed in this paper also provides some concrete hints for how mirror symmetry can be generalized to compactifications with arbitrary H-flux, whose mirrors are generically nongeometric.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,001 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.27 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We investigate a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop T-duality rules for NS-NS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced four-dimensional theory. The resulting structure is invariant under T-duality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included. This gives a concrete framework in which to investigate the possibility that generic string compactifications may be nongeometric in any duality frame. The framework developed in this paper also provides some concrete hints for how mirror symmetry can be generalized to compactifications with arbitrary H-flux, whose mirrors are generically nongeometric.

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 investigate a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes.	contribution 0.97	0.89	0.06	asserted 0.96
s1	These compactifications are nongeometric analogues of the twisted torus.	background 0.71	0.22	0.05	asserted 1.00
s2	We develop T-duality rules for NS-NS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced four-dimensional theory.	method 0.65	0.96	0.12	asserted 1.00
s3	The resulting structure is invariant under T-duality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included.	result 0.97	0.87	0.38	asserted 1.00
s4	This gives a concrete framework in which to investigate the possibility that generic string compactifications may be nongeometric in any duality frame.	interpretation 0.88	0.63	0.19	hedged possibility 0.85
s5	The framework developed in this paper also provides some concrete hints for how mirror symmetry can be generalized to compactifications with arbitrary H-flux, whose mirrors are generically nongeometric.	interpretation 0.69	0.80	0.11	hedged possibility 0.88

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 0.99.

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arXiv listing abstract v4

not examined

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levels run

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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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Dyonic ISO(7) supergravity and the duality hierarchy
hep-th 2015-08 accept novelty 6.0 of 10

The dyonic ISO(7) maximal supergravity has a family of stable anti-de Sitter vacua, including a new supersymmetric SU(3) vacuum and new non-supersymmetric ones, all catalogued with their scalar and vector mass spectra.
Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory
hep-th 2015-08 accept novelty 6.0 of 10

The Gomis-Ooguri non-relativistic closed string is shown to be a non-Riemannian Double Field Theory background whose sigma model and fluctuation spectrum match the Gomis-Ooguri results.
Minkowski 3-forms, Flux String Vacua, Axion Stability and Naturalness
hep-th 2015-07 conditional novelty 6.0 of 10

By dimensionally reducing Type II supergravity with fluxes, the authors show that all axion dependence of the flux potential flows through Minkowski 4-form auxiliary fields, which they argue forces corrections to appe...
A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory
hep-th 2015-03 conditional novelty 6.0 of 10

A flux-scaling construction stabilizes all closed-string moduli at tree level in non-supersymmetric, tachyon-free AdS vacua, but the same scaling that makes an axion light also pushes the heavy moduli above the Kaluza...
Geometry and fluxes of SL(5) exceptional field theory
hep-th 2014-12 accept novelty 6.0 of 10

The generalised torsion of a flat Weitzenböck connection on the SL(5) extended space reproduces the exceptional field theory action, and its irreducible parts are exactly the M-theory and IIB geometric and non-geometr...
Analytic Classes of Metastable de Sitter Vacua
hep-th 2014-06 accept novelty 6.0 of 10

A systematic procedure yields analytic families of locally stable de Sitter vacua in no-scale supergravity, and a no-go theorem shows that supersymmetric Minkowski vacua without flat directions cannot be continuously ...
On Inflation and de Sitter in Non-Geometric String Backgrounds
hep-th 2014-05 conditional novelty 6.0 of 10

Elliptic nongeometric fluxes in double field theory give potentials with Minkowski and de Sitter minima, and a toy quadratic inflation model whose slow roll requires fluxes tuned to about 10^-5.
Non-associative Deformations of Geometry in Double Field Theory
hep-th 2013-12 conditional novelty 6.0 of 10

In the flux formulation of double field theory, both candidate non-associative tri-product deformations reduce to total derivatives or vanish identically on-shell, so the effective action shows no associativity violation.
Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
hep-th 2013-07 accept novelty 6.0 of 10

Asymmetric freely-acting orbifolds of string theory generate non-geometric Q- and R-fluxes, and an explicit Z4xZ2 construction turns on all geometric and non-geometric fluxes simultaneously.
\beta-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
hep-th 2013-06 conditional novelty 6.0 of 10

A ten-dimensional supergravity theory is built whose non-geometric Q-flux is identified with a connection coefficient, yielding a second curvature scalar and explicit equations of motion.
Fully stable dS vacua from generalised fluxes
hep-th 2013-01 conditional novelty 6.0 of 10

A stochastic search finds three critical points of a type IIB flux superpotential with positive vacuum energy and all 14 mass eigenvalues positive.
On the distribution of stable de Sitter vacua
hep-th 2012-12 conditional novelty 6.0 of 10

In a six-parameter family of isotropic type IIB flux vacua with non-geometric flux, tachyon-free de Sitter critical points are a tiny fraction of all critical points and cluster in thin sheets near zero cosmological constant.
(Non-)commutative closed string on T-dual toroidal backgrounds
hep-th 2012-11 conditional novelty 6.0 of 10

On a non-geometric Q-flux torus, closed string coordinates Z1 and Z2 obey [Z1,Z2] = -i(2pi^2/3) N^3 H in the coincident-point limit, proportional to flux times winding.
Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
hep-th 2012-10 accept novelty 6.0 of 10

A bi-invariant Einstein-Hilbert-type action on the cotangent bundle reproduces the form of the standard string effective action under a Seiberg-Witten-type field redefinition, giving a geometric language for R-flux ba...
Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
hep-th 2012-07 conditional novelty 6.0 of 10

A membrane sigma-model on an R-flux background reduces to a twisted Poisson sigma-model on phase space whose boundary correlators reproduce Kontsevich's nonassociative star product, which also equals a Lie 2-group con...
Non-Geometric Fluxes in Supergravity and Double Field Theory
hep-th 2012-04 conditional novelty 6.0 of 10

Rewriting the ten-dimensional NSNS action in T-dual variables makes the non-geometric Q and R fluxes explicit, with R a covariant field strength of the bi-vector and Q the antisymmetric part of a dual connection.
Duality orbits of non-geometric fluxes
hep-th 2012-03 conditional novelty 6.0 of 10

All U-duality orbits of maximal gauged supergravities in D=8 and above have a geometric origin, while certain half-maximal T-duality orbits are non-geometric and require truly doubled double-field-theory compactifications.
Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory
hep-th 2012-02 accept novelty 6.0 of 10

Freely-acting asymmetric Z_N orbifolds give exactly solvable closed-string flux backgrounds whose toroidal coordinates obey a non-commutative algebra set by the non-geometric flux and the winding number around a circle.
A geometric action for non-geometric fluxes
hep-th 2012-02 conditional novelty 6.0 of 10

Inverting the generalized metric of double field theory turns the non-geometric Q flux into the antisymmetric part of a connection and the R flux into a covariant tensor obeying a Bianchi identity, yielding an action ...
The effective action of Double Field Theory
hep-th 2011-09 conditional novelty 6.0 of 10

A Scherk-Schwarz reduction of Double Field Theory on a twisted double torus reproduces the bosonic electric sector of four-dimensional gauged N=4 supergravity, with the gaugings identified as generalized fluxes of the twist.
Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
hep-th 2011-06 conditional novelty 6.0 of 10

At linear order in a constant three-form flux, closed-string tachyon amplitudes can be repackaged into a nonassociative tri-product, and the R-flux background is conjectured to flow to a left-right asymmetric conforma...
Charting the landscape of N=4 flux compactifications
hep-th 2011-02 conditional novelty 6.0 of 10

A complete classification of the vacua of the SO(3) truncation of N=4 flux compactifications shows that non-supersymmetric anti-de Sitter vacua can be stable and that a non-semisimple gauging admits a de Sitter critic...
T-duality and closed string non-commutative (doubled) geometry
hep-th 2010-10 conditional novelty 6.0 of 10

Closed string coordinates in twisted-torus and H-flux backgrounds fail to commute, with a commutator proportional to the string's momentum (or winding) in the third direction.
Smeared versus localised sources in flux compactifications
hep-th 2010-09 conditional novelty 6.0 of 10

BPS flux vacua with smeared sources survive localisation, but a class of non-BPS AdS solutions with smeared (anti-)D3-branes does not, undermining smeared-source non-BPS constructions.
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...
Complete classification of Minkowski vacua in generalised flux models
hep-th 2009-11 conditional novelty 6.0 of 10

A systematic scan of five generalised-flux supergravity models finds fully stable Minkowski and de Sitter vacua, with all moduli stabilised, only in the so(3,1)^2 model, and only when non-geometric fluxes are present.
D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades
hep-th 2009-06 accept novelty 6.0 of 10

Careful tracking of Page versus Maxwell versus brane charges implies the infrared B-field through the CP1 cycle of the ABJM/ABJ dual is b0 = -N4/k + 1/2, not -N4/k as previously claimed.
Non-geometric backgrounds, doubled geometry and generalised T-duality
hep-th 2009-02 accept novelty 6.0 of 10

Doubling all coordinates of a torus fibration, including the base circle, produces a twisted torus whose different polarisations reproduce geometric, T-fold, and R-flux string backgrounds.
On Slow-roll Moduli Inflation in Massive IIA Supergravity with Metric Fluxes
hep-th 2008-12 conditional novelty 6.0 of 10

For all but two of the standard toroidal orientifold compactifications of massive type IIA with metric fluxes, the slow-roll parameter epsilon is bounded below by a number of order one, excluding slow-roll inflation a...
T-duality, Generalized Geometry and Non-Geometric Backgrounds
hep-th 2008-07 conditional novelty 6.0 of 10

T-duality is realized as an O(d,d) rotation of generalized vielbeins and pure spinors, and the four-dimensional fluxes f, H, Q, R are identified with Courant-bracket structure constants of those vielbeins.
M-theory, exceptional generalised geometry and superpotentials
hep-th 2008-04 conditional novelty 6.0 of 10

N=1 M-theory backgrounds on seven-dimensional spaces are characterised by an element of the 912 representation of E_7(7), and the four-dimensional superpotential is an E_7(7)-invariant functional of this element.
Inflationary Constraints on Type IIA String Theory
hep-th 2007-11 accept novelty 6.0 of 10

In type IIA Calabi-Yau compactifications with standard fluxes, D6-branes and O6-planes at large volume and weak coupling, the slow-roll parameter obeys epsilon >= 27/13 wherever the potential is positive, so inflation...
The maximal D=4 supergravities
hep-th 2007-05 accept novelty 6.0 of 10

All gaugings of four-dimensional N=8 supergravity are encoded by an embedding tensor satisfying two group-theoretic constraints, with a universal Lagrangian that includes magnetic charges via 133 tensor gauge fields.
The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies
hep-th 2018-02 conditional novelty 5.0 of 10

The full classical flux potential of type IIA Calabi-Yau orientifolds factorizes into a bilinear form whose axion dependence is fixed by Freed-Witten anomalies of 4d string defects.
The Swampland Conjecture and F-term Axion Monodromy Inflation
hep-th 2017-03 conditional novelty 5.0 of 10

In every string model examined, delaying backreaction of the axion inflaton to trans-Planckian field ranges requires flux choices that push moduli masses above the Kaluza-Klein scale, so the effective theory breaks do...
Towards Axionic Starobinsky-like Inflation in String Theory
hep-th 2015-03 conditional novelty 5.0 of 10

A backreacted axion-monodromy potential in a type IIB flux toy model interpolates between quadratic and Starobinsky-like forms, but the Starobinsky regime requires a parameter choice that breaks single-field inflation.
NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
hep-th 2014-02 conditional novelty 5.0 of 10

The authors propose source-corrected Bianchi identities for the NS5-brane, KK-monopole and Q-brane, recover the sourceless identities from a nilpotent Dirac operator, and show that a class of geometric beta-supergravi...
Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
hep-th 2013-12 accept novelty 5.0 of 10

A quasi-Hopf algebra cochain twist yields a nonassociative star product on R-flux phase space, and 3-cyclicity of the phase-space integral makes a consistent nonassociative quantum mechanics possible, with area and vo...
The Spacetime of Double Field Theory: Review, Remarks, and Outlook
hep-th 2013-09 conditional novelty 5.0 of 10

Certain T-fold backgrounds with non-geometric fluxes are globally well-defined in double field theory because the required O(d,d;Z) monodromy transformations can be realized as generalized coordinate transformations.
Exploring Double Field Theory
hep-th 2013-04 conditional novelty 5.0 of 10

A flux formulation of Double Field Theory derives the strong-constraint-violating terms needed for non-geometric flux compactifications from a generalized curvature construction.
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...
Slow-Roll Inflation in Non-geometric Flux Compactification
hep-th 2013-02 conditional novelty 5.0 of 10

In a genetic search over non-geometric flux vacua, roughly ten stable de Sitter solutions appear, and two-dimensional slices of their scalar potentials show slow-roll parameters below one along a direction driven by t...
Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
hep-th 2012-07 conditional novelty 5.0 of 10

A Scherk-Schwarz reduction of SL(5) duality-invariant M-theory reproduces exactly the D=7 gauged supergravity potential and embedding tensor.
Gauged Double Field Theory
hep-th 2012-01 conditional novelty 5.0 of 10

The paper derives necessary and sufficient conditions for gauge invariance and algebra closure in Double Field Theory, and shows that compactification on twisted tori yields a gauged theory whose gaugings come from th...
Double Field Theory and N=4 Gauged Supergravity
hep-th 2011-09 conditional novelty 5.0 of 10

Compactifying Double Field Theory on a twisted doubled torus yields N=4 electric gauged supergravity, and the embedding-tensor closure conditions follow from a weaker differential constraint than the full strong constraint.
A ten-dimensional action for non-geometric fluxes
hep-th 2011-06 conditional novelty 5.0 of 10

A change of field variables recasts the ten-dimensional NSNS Lagrangian so that the non-geometric Q-flux appears explicitly, and dimensional reduction reproduces the known four-dimensional Q-flux potential.
3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
hep-th 2013-09 conditional novelty 4.0 of 10

A duality-invariant star-product on double phase space encodes the non-associativity of R-flux string vacua as a 3-cocycle, with a magnetic-monopole analogue in which only a single pole preserves angular momentum.
More stable dS vacua from S-dual non-geometric fluxes
hep-th 2013-04 conditional novelty 4.0 of 10

Explicit flux configurations on anisotropic tori yield 11 anti-de Sitter and 7 de Sitter vacua that are stable within a 14-real-modulus truncation, with the de Sitter cases stable only via the Breitenlohner-Freedman c...

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189 later papers cite it

Evidence: substantial. 186 of the citing papers share no author with it, and 21 of those carry a confident label from Pith's citation classifier.

Pith read 20 of the 409 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 used its method or tool.

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Used this paper's prescription, namely the orbifold of three tori with cyclic permutation, which identifies some moduli and parameters.

On Type IIB moduli stabilization and N = 4, 8 supergravities (2011) · 0.97 · paraphrased: the licence does not allow quoting

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179 arXiv papers cite this in 398 sentences

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Papers citing it · 265 sentences without a confident label

Builds on it 4 papers

To arrive at a duality invariant superpotential, the authors of [ref] started from the above described IIA case and performed the following steps: * T-dualize in the directions $(α, β, γ)$ to get to the IIB theory above.

Lie algebroids, non-associative structures and non-geometric fluxes · The four-dimensional perspective · 0.97
For constant fluxes a derivation was given in [ref] , but here we aim for the derivative corrections to these identities.

Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids · Introduction · 0.80
Including these new fluxes, the Gukov-Vafa-Witten superpotential [ref] can be extended in the following compact way [ref]

The Swampland Conjecture and F-term Axion Monodromy Inflation · Moduli stabilization and non-geometric fluxes · 0.82

Uses its method or tool 5 papers

Following the approach of [ref] , let us introduce a twisted differential acting on $p$-forms.

A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory · Twisted differential and Bianchi identities · 1.00
One way to derive these identities is via the Jacobi identities of the following Lie brackets for the NS-NS fluxes [ref] , [Z_i, Z_j ] = ω_ij^k Z_k - H_ijk X^k, [ Z_i, X^j ] = Q_i^jk Z_k - ω_ik^j X^k , [ X^i, X^j] = Q_k^ij X^k - R^ijk Z_k , where $Z_i$ and $X^i$'s are generators of the gauge transformations corresponding to the two gauge groups consisting of two sets of $d$-dimensional vectors obtained, from the metric and the $B$-field respectively, via the reduction of type II superstring theory on a $d$-dimensional torus.

On Missing Bianchi Identities in Cohomology Formulation · First formulation · 0.83
The prescription we use is that of [ref] , namely (T^2)^3 = T_(1)^2 ×T_(2)^2 ×T_(3)^2 / ℤ_3: T_(1)^2 →T_(2)^2 →T_(3)^2→T_(1)^2 .This identifies some of the moduli $T_i →T$ and $U_i →U$, and also some parameters (see Appendix), thus reducing the parameter space and making it simpler to look for solutions.

On Type IIB moduli stabilization and N = 4, 8 supergravities · Excluding regions of the parameter space · 0.97

Uses its data or values 1 paper

Here is the superpotential of a typical system, taken from [ref] .

A Simple Introduction to Grobner Basis Methods in String Phenomenology · Constraints · 0.85

Compares with it 10 papers

Comparing this potential, using the decomposition ([ref]) and the parametrization ([ref]), with those obtained from Scherk-Schwarz reductions with fluxes [ref] as well as with their non-geometric generalizations [ref] , leads us to identify $H_abc$ with the standard NS-NS flux, $τ_ab^abc$ with the geometric flux, $Q_c^cab$ with the locally geometric flux and $R^abc$ with the so-called non-geometric flux.

Conformal chiral boson models on twisted doubled tori and non-geometric string vacua · Twisted doubled tori and $N=4$ gauged supergravities · 1.00
* For constant fluxes, the five Bianchi identities above reduce to the system of Bianchi identities derived in [ref] which, in our notation, read

Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids · Remarks · 0.91
So we have agreement with [ref] where it was conjectured the $H$ structure constants would be transformed into these $Q$ structure constants.

Non-geometric String Backgrounds and Worldsheet Algebras · Q-space · 0.87

Cites it as support 3 papers

It turns out that adding these extra ingredients really does alleviate some of the problems mentioned above [ref] .

D-Terms from Generalized NS-NS Fluxes in Type II · Introduction · 1.00
In particular, there is evidence that many massive, gauged supergravities cannot be naturally embedded in string theory without such a framework [ref] .

Flux compactifications, twisted tori and doubled geometry · Introduction · 0.98
This observation supports one of the main initial motivations for introducing non-geometric fluxes [ref] , namely the consistency of fluxes with T-duality.

Dimensional Oxidation of Non-geometric Fluxes in Type II Orientifolds · Counting terms for type IIB · 0.99

Cites it as background 81 papers

They arise from type IIB generalised flux compactifications on $𝕋^6/ (ℤ_2 ×ℤ_2)$ isotropic orientifolds with O3/O7-planes [ref] .

Complete classification of Minkowski vacua in generalised flux models · The $𝒩=1$ SUGRA models · 0.86
One formulation involves fluxes denoted by the real six dimensional indices (e.g. $H_ijk$ etc.) [ref] while in the latter one, all flux components are written out using cohomology indices of the complex threefold $X_3$; e.g. $H_K, ω_a K$ etc., where $K ∈{0, 1, ..,h^2,1(X_3)}$ and $a ∈{1, 2, .., h^1,1_-(X_3) }$ [ref] .

On Missing Bianchi Identities in Cohomology Formulation · Introduction · 0.92
As opposed to KKLT and the LVS scenario these moduli are also stabilized at tree-level by turning on non-geometric $Q$-flux [ref] . * In [ref] the proposal was to consider the two-forms $B_2$ or $C_2$ as the inflaton.

A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory · Axion monodromy inflation · 0.81

Discussion

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