Generalised T-Duality and Non-Geometric Backgrounds

Atish Dabholkar; Chris Hull

REVIEW

Generalised T-Duality and Non-Geometric Backgrounds

Atish Dabholkar, Chris Hull

High Energy Physics - Theory · Submitted 1 Dec 2005 · 30 references

Pith's verdict: The paper that opened the Q/R flux story; the derivations are clean, but the general both-twist backgrounds are proposed, not constructed, and the authors say so.

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CitationAtish Dabholkar, Chris Hull. "Generalised T-Duality and Non-Geometric Backgrounds." arXiv:hep-th/0512005 (2005). https://pith.science/paper/SYS2PAOQ

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Editor's note

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This is the paper that put dual-coordinate dependence on the map, and it deserves the reputation it has. The core move — take a T-fold or a twisted torus, T-dualise along the circle that carries the twist even though there is no isometry, and land on a background that depends on ỹ as well as y — is the right idea, and it is what later became the Q- and R-flux classification. The gauge algebra of §3, the universal potential (2.14), and the SO(3) WZW check in §6 are the parts I trust most. The WZW check is a real independent test: the potential's cubic term with no quadratic term, the single flat direction, the breaking to SO(2)×SO(2) — that is not something you get for free from covariance, and it is the strongest evidence in the paper that (2.14) is the right object. The T-dual-of-a-consistent-background argument is also solid as far as it goes: if the seed is consistent, the dual is consistent, full stop. Where I would push back is on the abstract's 'we find a new class' (abstract:s1). What is actually constructed is the class reachable by T-duality from known backgrounds, plus the orbifold points of §7.1. The general case with both a y-twist and a ỹ-twist (8.7) is argued by the polarisation-change step in §8 — 'one can simply choose the other polarisation' — and that step is established for the torus in [1], not for a bundle with y-dependent moduli. The stress-test note is right that this is the load-bearing extrapolation, and right that no sigma-model, partition function, or SFT solution with ỹ-dependence is written down. But the authors are not hiding this: §7 postpones modular invariance, §7.2 says the analysis is entirely classical, and §9.2 says the doubled geometry will be explored elsewhere. So the honest reading is that the paper claims a proposal plus a consistency argument, and the abstract oversells it by one notch. That is a wording issue, not a soundness issue. The potential's universality is likewise inferred from O(d,d) covariance plus matching Scherk-Schwarz rather than proven, but the WZW check makes that inference credible. Who should read it: anyone working on non-geometric flux compactifications, doubled/generalised geometry, or flux mirror symmetry. It is a foundational reference, not a self-contained construction. Send it to referees — the parts that need scrutiny are the polarisation argument and the claim that the potential is universal in any dimension, and both are worth a careful report.

Referee report

Significance

If the central claim holds, T-duality is an exact symmetry of string theory on a much larger class of backgrounds than the Buscher rules allow, and flux compactifications, T-folds, and the new dual-coordinate-dependent backgrounds sit in a single framework. The concrete results — the gauge algebra (3.4), the potential (2.14), and the WZW check of §6 — are useful independently of the more speculative parts, and the paper has been influential in the non-geometric backgrounds literature. The WZW check is a genuine independent test: the WZW model is not a Scherk–Schwarz reduction, so the reproduction of the cubic term and, more importantly, the vanishing of the quadratic term in (6.3) is non-trivial evidence for the proposed potential rather than a restatement of it.

Major objections (4)

[§2, Eqs. (2.13)–(2.14)] The paper fixes the four constants a, b, c, d in the general potential (2.13) by requiring agreement with the Scherk–Schwarz potential W_SS and then asserts that the same coefficients apply to all supersymmetric gaugings. This universality is an assumption about the space of gaugings rather than a derivation from supersymmetry, and it is load-bearing for the WZW analysis of §6 and the duality-twist discussion of §7. The paper would be stronger if it stated this explicitly and pointed to §6 as the independent test: the WZW model is not a Scherk–Schwarz reduction, so the reproduction of the cubic term and the absence of a quadratic term in (6.3) is genuine evidence for (2.14) rather than a restatement of it. I would ask the authors to make that logical structure explicit in §2.
[§8, Eq. (8.7)] The existence claim for backgrounds with simultaneous y- and ỹ-twists rests on the polarisation-change argument ('in this doubled picture one can simply choose the other polarisation'). For the torus this is established in [1], but for a bundle with y-dependent moduli the doubled geometry is a bundle over the doubled base, and the equivalence of polarisations is extended by analogy rather than derived. The authors acknowledge the limitation in §7.2 ('our analysis here is entirely classical and the quantum consistency of the theory is not guaranteed') and in §9.2 ('This geometry will be explored further elsewhere'), so the issue is not concealment but framing: the abstract's 'we find a new class of non-geometric backgrounds' is stronger than the 'we argue that T-duality acts' of the following sentence. The established cases are T-duals of consistent backgrounds and asymmetric-orbifold points at the potential minimum; the general (8.7) case should be labelled as a proposal in the abstract and introduction.
[§6, Eq. (6.3) and reference [29]] The abstract claims 'the complete non-linear structure for a class of WZW-model deformations', but the check performed here is at leading order in φ: the cubic term and the vanishing quadratic term are reproduced, while the statement that the flat direction is exact is deferred to [29], which is listed as 'in preparation'. Since [29] is not available to the reader, the present paper establishes the flat direction only to the order shown. Either the exact statement should be supported within this paper, or the abstract and §6 should be qualified to say that exactness is argued and will be demonstrated in [29].
[§6, after Eq. (6.3)] The paper reports that at the would-be minimum φ = δ_{α3}δ_{α'3}v, 'two become massive and two become tachyonic'. A point with tachyonic directions is not a minimum, and the identification of this point as the vacuum about which the symmetry-breaking pattern is read off needs qualification. In the exact WZW model the deformation ∫a J³J̃³ is exactly marginal and the deformed theory is unitary, so the tachyons are presumably an artifact of the truncation to the gauged supergravity; the paper should say so explicitly, or explain why the tachyonic directions are absent in the full potential.

Minor objections (6)

[§1, §7.1, §10, Eq. (4.10)] There are several typographical errors: 'lifiings' in the penultimate paragraph of §1, 'the the dual' in §7.1, and a stray '∧' in the B-field ansatz (4.10). In §10, 'momentum modes would be sensitive to the ỹ-dependence' should read 'winding modes', since the sentence contrasts momentum and winding probes.
[Eq. (5.5)] The exponent a = 6/(D-1)(D-2) should be bracketed as 6/((D-1)(D-2)) to avoid the reading 6(D-2)/(D-1). The symbol K in (5.5) should also be distinguished from the scalar matrix K_ab used in §2.
[§3, Eq. (3.4)] The Jacobi constraints on the general tensors γ, β, γ̃, β̃, γ̂, γ̄ are referred to but not written out. Since the paper claims to give 'the general set of parameters' specifying the low-energy theory, listing the constraints explicitly would make the classification usable.
[§5 and §7] The statement that (2.14) reduces to (5.5) when the structure constants take the form (5.4) is asserted as 'easy to see'. A one-line verification would help the reader confirm that the duality-twist potential is indeed a special case of the general formula.
[§9.2] The relation to generalised geometry is deferred to future work ('This geometry will be explored further elsewhere'). The abstract's 'readily formulated in terms of a doubled geometry, related to generalised geometry' could be softened accordingly, since the geometry is sketched rather than developed here.
[References [13] and [29]] Both references are listed as 'in preparation'. The reliance on [29] for the exact flat direction is noted in the major comments; the reliance on [13] for the type II reduction is less central but should be flagged where it is used.

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The paper

The paper claims

T-duality is extended to backgrounds where no circle is an isometry, producing spaces that depend on winding coordinates.

The reading

String theory's T-duality is normally a set of rules that only applies when the direction you dualise is a symmetry of the background. This paper asks what happens when it is not, and answers that T-duality still acts, but the result is not a conventional space at all: it depends on the coordinate conjugate to string winding number, so it has no local spacetime description even patch by patch. The authors argue that such backgrounds are forced on us, because T-dualising a three-torus with constant $H$-flux three times must land somewhere, and the third step has no isometry to work with. They give the construction a home in string field theory and in a doubled geometry with coordinates for both momentum and winding, and they show that at special points in moduli space the same objects reduce to asymmetric orbifolds that are already known to be consistent string backgrounds.

What carries the argument

The load-bearing device is the doubled geometry: a torus $T^d$ is promoted to a doubled torus with coordinates $y^i$ and dual coordinates $x_i$, and the T-duality group $O(d,d;Z)$ acts geometrically on the doubled torus even when it acts non-geometrically on $y$ alone. A duality-twisted reduction with monodromy $M$ becomes a bundle over a doubled base, and T-duality is a change of which coordinate is called spacetime. The second device is the scalar potential $W(K) = (1/12) K^{ad} K^{be} K^{cf} f_{abc} f_{def} - (1/4) K^{ad} L^{be} L^{cf} f_{abc} f_{def}$, fixed by matching the Scherk-Schwarz result of Kaloper and Myers and then extended by $O(d,d)$ covariance to arbitrary gaugings; its cubic term in the WZW case gives the determinant form of the Higgs field and the correct flat direction.

Extended reading notes

Core claim

The central claim is that there is a class of non-geometric string backgrounds with genuine dependence on the dual coordinates conjugate to winding number, sitting alongside ordinary flux compactifications and T-folds. T-folds are locally ordinary spacetimes glued by T-duality transition functions; the new backgrounds are stranger, since even locally they are not manifolds. The authors argue that a generalised T-duality acts on this wider class, taking a twisted-torus flux compactification or a T-fold to one of the new backgrounds, and that this is the missing third T-duality of $T^3$ with constant $H$-flux, where the base circle is not an isometry. The mechanism is a change of polarisation in a doubled formalism: the conformal field theory carries both momentum and winding labels, one chooses which coordinate to call spacetime, and the physics is claimed to be independent of that choice. They further construct the bosonic sector of the corresponding gauged supergravities in any dimension, with a universal scalar potential quadratic in the embedding tensor, and check it against the $SO(3)$ WZW model, where the potential reproduces the expected symmetry breaking to $SO(2)$ times $SO(2)$ with a single flat direction.

Load-bearing premise

The construction is classical throughout, and the claim that these dual-coordinate-dependent backgrounds are genuine string backgrounds rests on assuming that the doubled-formalism solutions lift to modular-invariant quantum theories away from the special moduli points where they reduce to known asymmetric orbifolds.

Editorial extensions

If this is right

Mirror symmetry for Calabi-Yau manifolds with $T^3$ fibration and $H$-flux would have a concrete non-geometric mirror, obtained by T-dualising all fibre directions, as the Strominger-Yau-Zaslow picture suggests when flux is included.
Gauged supergravities whose non-abelian gauge fields come from the antisymmetric tensor, rather than from isometries of the internal metric, acquire classical string liftings, removing an apparent obstruction to lifting a wide class of effective theories.
The universal potential gives a complete nonlinear description of a class of WZW-model deformations, including the leading $1/k$ correction to the central charge, which is otherwise an $\alpha'$ effect invisible to supergravity.
Every background reached by these generalised dualities inherits the quantum consistency of the background it came from, so T-duals of consistent T-folds are consistent even when no sigma-model metric can be written.

Reading between the lines

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

If dual-coordinate dependence is real, momentum modes and winding modes probe different effective geometries of the same background, which suggests that any operational definition of the spacetime in these models must specify the probe, a point the paper raises but does not resolve.
The construction predicts that the localised NS5-brane on a circle and the Kaluza-Klein monopole are related by a duality that produces dual-coordinate dependence in the monopole, matching the world-sheet instanton computations cited from Gregory-Harvey-Moore and Tong; a direct check of the full nonlinear map would be a sharp test.
Because the doubled torus is a genuine manifold with an $SL(2d;Z)$ action, one could ask whether the doubled description admits a variational principle and a well-defined path integral of its own, which would make the polarisation-independence claim into a theorem rather than a bookkeeping device.
Extending the same logic to U-duality would replace winding by brane wrapping, so the analogous exotic backgrounds would depend on coordinates conjugate to membrane and fivebrane charges; the paper flags this as future work, and it is where the classical treatment is most likely to fail first.

Original abstract

We undertake a systematic analysis of non-geometric backgrounds in string theory by seeking stringy liftings of a class of gauged supergravity theories. In addition to conventional flux compactifications and non-geometric T-folds with T-duality transition functions, we find a new class of non-geometric backgrounds with non-trivial dependence on the dual coordinates that are conjugate to the string winding number. We argue that T-duality acts in our class of theories, including those cases without isometries in which the conventional Buscher rules cannot be applied, and that these generalised T-dualities can take T-folds or flux compactifications on twisted tori to examples of the new non-geometric backgrounds. We show that the new class of non-geometric backgrounds and the generalised T-dualities arise naturally in string field theory, and are readily formulated in terms of a doubled geometry, related to generalised geometry. At special points in moduli space, some of the non-geometric constructions become equivalent to asymmetric orbifolds which are known to provide consistent string backgrounds. We construct the bosonic sector of the corresponding gauged supergravity theories and show that they have a universal form in any dimension, and in particular construct the scalar potential. We apply this to the supersymmetric WZW model, giving the complete non-linear structure for a class of WZW-model deformations.

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The abstract, sentence by sentence

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

We undertake a systematic analysis of non-geometric backgrounds in string theory by seeking stringy liftings of a class of gauged supergravity theories. In addition to conventional flux compactifications and non-geometric T-folds with T-duality transition functions, we find a new class of non-geometric backgrounds with non-trivial dependence on the dual coordinates that are conjugate to the string winding number. We argue that T-duality acts in our class of theories, including those cases without isometries in which the conventional Buscher rules cannot be applied, and that these generalised T-dualities can take T-folds or flux compactifications on twisted tori to examples of the new non-geometric backgrounds. We show that the new class of non-geometric backgrounds and the generalised T-dualities arise naturally in string field theory, and are readily formulated in terms of a doubled geometry, related to generalised geometry. At special points in moduli space, some of the non-geometric constructions become equivalent to asymmetric orbifolds which are known to provide consistent string backgrounds. We construct the bosonic sector of the corresponding gauged supergravity theories and show that they have a universal form in any dimension, and in particular construct the scalar potential. We apply this to the supersymmetric WZW model, giving the complete non-linear structure for a class of WZW-model deformations.

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 undertake a systematic analysis of non-geometric backgrounds in string theory by seeking stringy liftings of a class of gauged supergravity theories.	contribution 0.94	0.95	0.08	asserted 0.89
s1	In addition to conventional flux compactifications and non-geometric T-folds with T-duality transition functions, we find a new class of non-geometric backgrounds with non-trivial dependence on the dual coordinates that are conjugate to the string winding number.	result 0.89	0.95	0.23	asserted 1.00
s2	We argue that T-duality acts in our class of theories, including those cases without isometries in which the conventional Buscher rules cannot be applied, and that these generalised T-dualities can take T-folds or flux compactifications on twisted tori to examples of the new non-geometric backgrounds.	result 0.44	0.84	0.39	asserted 0.74
s3	We show that the new class of non-geometric backgrounds and the generalised T-dualities arise naturally in string field theory, and are readily formulated in terms of a doubled geometry, related to generalised geometry.	result 0.64	0.92	0.17	asserted 1.00
s4	At special points in moduli space, some of the non-geometric constructions become equivalent to asymmetric orbifolds which are known to provide consistent string backgrounds.	result 0.95	0.68	0.07	asserted 0.76
s5	We construct the bosonic sector of the corresponding gauged supergravity theories and show that they have a universal form in any dimension, and in particular construct the scalar potential.	contribution 0.66	0.97	0.09	asserted 1.00
s6	We apply this to the supersymmetric WZW model, giving the complete non-linear structure for a class of WZW-model deformations.	contribution 0.79	0.95	0.07	asserted 1.00

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

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arXiv listing abstract v2

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full text
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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

Works cited (30)

[1]

C. M. Hull, JHEP 0510 (2005) 065, arXiv:hep-th/0406102

View on Pith Pith review arXiv 2005
[29]

A. Dabholkar and C. Hull, in preparation

View on Pith
[2]

A. Dabholkar and C. Hull, JHEP 0309, 054 (2003) [arXiv:hep-th/0210209]

View on Pith Pith review arXiv 2003
[3]

A. Flournoy, B. Wecht and B. Williams, arXiv:hep-th/040 4217

View on Pith
[4]

S. Kachru, M. B. Schulz, P. K. Tripathy and S. P. Trivedi, J HEP 0303, 061 (2003) [arXiv:hep-th/0211182]

View on Pith Pith review arXiv 2003
[5]

S. Hellerman, J. McGreevy and B. Williams, JHEP 0401, 024 (2004) [arXiv:hep-th/0208174]

View on Pith Pith review arXiv 2004
[6]

D. A. Lowe, H. Nastase and S. Ramgoolam, Nucl. Phys. B 667 (2003) 55 [arXiv:hep-th/0303173]

View on Pith Pith review arXiv 2003
[7]

A. Flournoy and B. Williams, arXiv:hep-th/0511126

View on Pith Pith review arXiv
[8]

J. Shelton, W. Taylor and B. Wecht, arXiv:hep-th/050813 3

View on Pith
[9]

J. Gray and E. Hackett-Jones, arXiv:hep-th/0506092

View on Pith Pith review arXiv
[10]

C. M. Hull, JHEP 9811, 027 (1998) [arXiv:hep-th/9811021]

View on Pith Pith review arXiv 1998
[11]

A. Strominger, S. T. Yau and E. Zaslow, Nucl. Phys. B 479, 243 (1996) [arXiv:hep-th/9606040]

View on Pith Pith review arXiv 1996
[12]

N. Kaloper and R. C. Myers, JHEP 9905, 010 (1999) [arXiv:hep-th/9901045]. 26

View on Pith Pith review arXiv 1999
[13]

C. M. Hull and R. Reid-Edwards, in preparation

View on Pith
[14]

A. Giveon, N. Malkin and E. Rabinovici, Phys. Lett. 238 (1990) 57

View on Pith 1990
[15]

C. M. Hull and R. A. Reid-Edwards, arXiv:hep-th/050311 4

View on Pith
[16]

J. Scherk and J. H. Schwarz, Nucl. Phys. B 153, 61 (1979)

View on Pith 1979
[17]

J. Maharana and J.H. Schwarz, Nucl. Phys. B390 (1993) 3 [hep-th/9207016]

View on Pith Pith review arXiv 1993
[18]

M. Cvetic, G. W. Gibbons, H. Lu and C. N. Pope, Class. Quan t. Grav. 20, 5161 (2003) [arXiv:hep-th/0306043]

View on Pith Pith review arXiv 2003
[19]

T.H. Buscher, Phys. Lett. B194 (1987) 59; Phys. Lett. B201 (1988) 466

View on Pith 1987
[20]

K. S. Narain, M. H. Sarmadi and C. Vafa, Nucl. Phys. B 288, 551 (1987)

View on Pith 1987
[21]

A. Dabholkar and J. A. Harvey, JHEP 9902, 006 (1999) [arXiv:hep-th/9809122]

View on Pith Pith review arXiv 1999
[22]

T. Kugo and B. Zwiebach, Prog. Theor. Phys. 87, 801 (1992) [arXiv:hep-th/9201040]

View on Pith Pith review arXiv 1992
[23]

M. Evans and I. Giannakis, Nucl. Phys. B 472 (1996) 139 [arXiv:hep-th/9511061]

View on Pith Pith review arXiv 1996
[24]

R. Gregory, J. A. Harvey and G. W. Moore, Adv. Theor. Math . Phys. 1, 283 (1997) [arXiv:hep-th/9708086]

View on Pith Pith review arXiv 1997
[25]

D. Tong, JHEP 0207, 013 (2002) [arXiv:hep-th/0204186]

View on Pith Pith review arXiv 2002
[26]

J. A. Harvey and S. Jensen, arXiv:hep-th/0507204

View on Pith Pith review arXiv
[27]

K. Okuyama, JHEP 0508 (2005) 089 [arXiv:hep-th/0508097]

View on Pith Pith review arXiv 2005
[28]

C. M. Hull and P. K. Townsend, Nucl. Phys. B 438, 109 (1995) [arXiv:hep-th/9410167]

View on Pith Pith review arXiv 1995
[30]

N. Hitchin, Quart. J. Math. Oxford Ser. 54, 281 (2003) [arXiv:math.dg/0209099]. 27

View on Pith arXiv 2003

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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.
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.
Doubled Geometry and T-Folds
hep-th 2006-05 conditional novelty 6.0 of 10

The doubled, T-duality-covariant string formalism is shown to be quantum-equivalent to the conventional sigma-model for world-sheets of any genus, once half the constraint currents are gauged and a topological term is added.
Gauged N=4 supergravities
hep-th 2006-02 conditional novelty 6.0 of 10

The authors give the general Lagrangian, Killing spinor equations, and scalar potential for gauged N=4 supergravity in four and five dimensions, parameterized by constrained embedding tensors, and show how the five-di...
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...
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.
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.
A Double Sigma Model for Double Field Theory
hep-th 2011-11 conditional novelty 5.0 of 10

The one-loop beta function of a doubled-target-space sigma model vanishes exactly when the generalized Ricci tensor of double field theory vanishes, making double field theory its effective field theory.
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.
Lectures on Nongeometric Flux Compactifications
hep-th 2007-08 conditional novelty 2.0 of 10

T-duality applied to ordinary flux compactifications requires nongeometric fluxes, and the notes assemble the resulting duality-invariant superpotential and its constraints.
Duality Symmetric String and M-Theory
hep-th 2013-06 accept

The paper is a review that connects the doubled worldsheet, Double Field Theory, and exceptional generalised geometry as one program for making T- and U-duality manifest.

How later papers used it

78 later papers cite it

Evidence: some. 74 of the citing papers share no author with it, and 3 of those carry a confident label from Pith's citation classifier.

Pith read 21 of the 151 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. 2 more papers by the same authors are listed: 1 built on it and 1 used its method or tool.

Builds on it 2 of 3 papers with this label · 1 by the same authors

Extended this paper's results and showed that all fluxes appearing in M-theory compactifications on manifolds with SU(3) structure that gauge isometries in the vector multiplet sector have a correspondent in heterotic compactifications with duality twists.

Heterotic type IIA duality with fluxes - towards the complete story (2010) · 0.91 · paraphrased: the licence does not allow quoting

By the same authors

Extended the Buscher transformation to the case with dependence on both x and x, providing a generalisation of T-duality of the kind proposed in this paper.

Double Field Theory (2009) (same authors) · 0.84 · paraphrased: the licence does not allow quoting

Uses its method or tool 1 of 2 papers with this label · 1 by the same authors

By the same authors

Used a generalised T-duality from this paper, which takes a background with dependence on x to an essentially doubled background whose fields depend on the coordinate of the T-dual circle.

Noncommutative gauge theories on D-branes in non-geometric backgrounds (2019) (same authors) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

72 arXiv papers cite this in 144 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 · 99 sentences without a confident label

Builds on it 3 papers

In section [ref] we extended the results in [ref] and showed that all the fluxes which appear in M-theory compactifications on manifolds with $SU(3)$ structure and which gauge isometries in the vector multiplet sector have a correspondent in heterotic compactifications with duality twists as discussed in [ref] .

Heterotic type IIA duality with fluxes - towards the complete story · Conclusions · 0.91
This example with $R$-flux arose from the replacement ([ref]) of $x$ with $x$ in the T-fold generalised metric ([ref]), so that it may be viewed as a $T^2$ fibration over the dual coordinate $x̃∼𝕏^1$ [ref] .

Non-geometric backgrounds, doubled geometry and generalised T-duality · R-Flux · 0.81
The Buscher transformation of $$ was extended to the case with dependence on both $x$ and $x$, providing a generalisation of T-duality of the kind proposed in [ref] .

Double Field Theory · Spaces large and small · 0.84

Uses its method or tool 2 papers

For such cases, we use a generalised T-duality [ref] which takes a background with dependence on $x$ to an essentially doubled background in which the fields depend on the coordinate $$ of the T-dual circle and so are problematic to interpret in conventional terms.

Noncommutative gauge theories on D-branes in non-geometric backgrounds · D-branes and doubled twisted torus geometry · 0.98
For the three-dimensional backgrounds considered here there is no isometry, even locally, in the $x$-direction, so we cannot use the Buscher rules, even on a cover of the space; however, in section three we shall perform a non-isometric or `generalised duality' along the lines of that of [ref] and suggest another dual description of this background.

Flux compactifications, twisted tori and doubled geometry · T-duality and T-folds · 0.81

Compares with it 1 paper

It will be argued that the $Q$-flux is akin to that found for the T-folds studied in [ref] where the monodromy around the $T^2$ cycles include a strict T-duality and mixes metric and $B$-field degrees of freedom.

N=4 Gauged Supergravity from Duality-Twist Compactifications of String Theory · Introduction · 0.93

Cites it as support 3 papers

However, there is some evidence that there should be a generalisation of T-duality that applies to the case of a torus fibration where the torus action is not isometric [ref] .

Non-geometric backgrounds, doubled geometry and generalised T-duality · Introduction · 0.97
Evidence for such a non-isometric T-duality was given in [ref] .

Flux compactifications, twisted tori and doubled geometry · Non-geometric backgrounds and gauged supergravity · 0.97
Furthermore, there is evidence that the existence of an isometry, even locally, is not a requirement for T-duality to be possible [ref] .

N=4 Gauged Supergravity from Duality-Twist Compactifications of String Theory · Conclusion, Discussion and Future Directions · 0.99

Cites it as background 30 papers

The doubled formalism [ref] was introduced to describe string backgrounds with a toroidal fibre in a manner which makes the T-duality action on the fibre into a manifest symmetry of a sigma model.

A Double Sigma Model for Double Field Theory · Relation to the doubled formalism · 0.97
In order to rewrite the string sigma model in a way in which T-duality is manifest, Hull introduced the doubled formalism [ref] .

Connecting T-duality invariant theories · The doubled formalism · 0.97
For non-isometric directions, there is a notion of generalised T-duality that can be applied [ref] .

Noncommutative gauge theories on D-branes in non-geometric backgrounds · Introduction and summary · 0.81

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.

[1] [1]

C. M. Hull, JHEP 0510 (2005) 065, arXiv:hep-th/0406102

View on Pith Pith review arXiv 2005

[2] [29]

A. Dabholkar and C. Hull, in preparation

View on Pith

[3] [2]

A. Dabholkar and C. Hull, JHEP 0309, 054 (2003) [arXiv:hep-th/0210209]

View on Pith Pith review arXiv 2003

[4] [3]

A. Flournoy, B. Wecht and B. Williams, arXiv:hep-th/040 4217

View on Pith

[5] [4]

S. Kachru, M. B. Schulz, P. K. Tripathy and S. P. Trivedi, J HEP 0303, 061 (2003) [arXiv:hep-th/0211182]

View on Pith Pith review arXiv 2003

[6] [5]

S. Hellerman, J. McGreevy and B. Williams, JHEP 0401, 024 (2004) [arXiv:hep-th/0208174]

View on Pith Pith review arXiv 2004

[7] [6]

D. A. Lowe, H. Nastase and S. Ramgoolam, Nucl. Phys. B 667 (2003) 55 [arXiv:hep-th/0303173]

View on Pith Pith review arXiv 2003

[8] [7]

A. Flournoy and B. Williams, arXiv:hep-th/0511126

View on Pith Pith review arXiv

[9] [8]

J. Shelton, W. Taylor and B. Wecht, arXiv:hep-th/050813 3

View on Pith

[10] [9]

J. Gray and E. Hackett-Jones, arXiv:hep-th/0506092

View on Pith Pith review arXiv

[11] [10]

C. M. Hull, JHEP 9811, 027 (1998) [arXiv:hep-th/9811021]

View on Pith Pith review arXiv 1998

[12] [11]

A. Strominger, S. T. Yau and E. Zaslow, Nucl. Phys. B 479, 243 (1996) [arXiv:hep-th/9606040]

View on Pith Pith review arXiv 1996

[13] [12]

N. Kaloper and R. C. Myers, JHEP 9905, 010 (1999) [arXiv:hep-th/9901045]. 26

View on Pith Pith review arXiv 1999

[14] [13]

C. M. Hull and R. Reid-Edwards, in preparation

View on Pith

[15] [14]

A. Giveon, N. Malkin and E. Rabinovici, Phys. Lett. 238 (1990) 57

View on Pith 1990

[16] [15]

C. M. Hull and R. A. Reid-Edwards, arXiv:hep-th/050311 4

View on Pith

[17] [16]

J. Scherk and J. H. Schwarz, Nucl. Phys. B 153, 61 (1979)

View on Pith 1979

[18] [17]

J. Maharana and J.H. Schwarz, Nucl. Phys. B390 (1993) 3 [hep-th/9207016]

View on Pith Pith review arXiv 1993

[19] [18]

M. Cvetic, G. W. Gibbons, H. Lu and C. N. Pope, Class. Quan t. Grav. 20, 5161 (2003) [arXiv:hep-th/0306043]

View on Pith Pith review arXiv 2003

[20] [19]

T.H. Buscher, Phys. Lett. B194 (1987) 59; Phys. Lett. B201 (1988) 466

View on Pith 1987

[21] [20]

K. S. Narain, M. H. Sarmadi and C. Vafa, Nucl. Phys. B 288, 551 (1987)

View on Pith 1987

[22] [21]

A. Dabholkar and J. A. Harvey, JHEP 9902, 006 (1999) [arXiv:hep-th/9809122]

View on Pith Pith review arXiv 1999

[23] [22]

T. Kugo and B. Zwiebach, Prog. Theor. Phys. 87, 801 (1992) [arXiv:hep-th/9201040]

View on Pith Pith review arXiv 1992

[24] [23]

M. Evans and I. Giannakis, Nucl. Phys. B 472 (1996) 139 [arXiv:hep-th/9511061]

View on Pith Pith review arXiv 1996

[25] [24]

R. Gregory, J. A. Harvey and G. W. Moore, Adv. Theor. Math . Phys. 1, 283 (1997) [arXiv:hep-th/9708086]

View on Pith Pith review arXiv 1997

[26] [25]

D. Tong, JHEP 0207, 013 (2002) [arXiv:hep-th/0204186]

View on Pith Pith review arXiv 2002

[27] [26]

J. A. Harvey and S. Jensen, arXiv:hep-th/0507204

View on Pith Pith review arXiv

[28] [27]

K. Okuyama, JHEP 0508 (2005) 089 [arXiv:hep-th/0508097]

View on Pith Pith review arXiv 2005

[29] [28]

C. M. Hull and P. K. Townsend, Nucl. Phys. B 438, 109 (1995) [arXiv:hep-th/9410167]

View on Pith Pith review arXiv 1995

[30] [30]

N. Hitchin, Quart. J. Math. Oxford Ser. 54, 281 (2003) [arXiv:math.dg/0209099]. 27

View on Pith arXiv 2003