A Geometry for Non-Geometric String Backgrounds

C M Hull

REVIEW

A Geometry for Non-Geometric String Backgrounds

C M Hull

High Energy Physics - Theory · Submitted 11 Jun 2004 · 48 references

Pith's verdict: The geometric core is right and has aged well; the 'string formulation' in the title is a classical statement, and Hull says so in §8.

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arXiv IDhep-th/0406102 (version 3)

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CitationC M Hull. "A Geometry for Non-Geometric String Backgrounds." arXiv:hep-th/0406102 (2004). https://pith.science/paper/OTC4AAUM

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Editor's note

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The thing to take away: Hull recasts a T-fold as a geometric T^{2n} bundle over the same base, with physical spacetime a locally chosen null T^n slice of each fibre. T-duality then becomes a change of which slice is physical, and 'non-geometric' becomes the precise statement that the local slices do not glue into a global T^n sub-bundle. That reframing is the contribution, and it is the reason people still cite this paper. It is not a repackaging of his earlier T-fold work [1,10,11]; the polarization machinery in §5 is new and it is what makes the rest work. The product-structure characterization (integral R with R^2=1, pseudo-hermitian w.r.t. L) is a clean bijection, and the D-brane discussion in §7 falls out of it without strain, including the p -> p' change across a transition function, which is the sort of thing that usually has to be bolted on by hand. The n=1 case in §3.1 is a real external check: the Buscher rules (3.10),(3.11) come back out of the doubled formalism, and §2.4 does the elimination of ~X explicitly rather than gesturing at it. I would not call §6 qualitative, by the way — the argument that O(n,n;Z) does not reduce to GL(n;Z) is the standard non-reducibility statement and it is enough for the claim being made. A worked example with an explicit obstruction would be nice, not necessary. The soft spot is the one the paper itself flags. 'Physics is independent of polarization' is a quantum statement, and it needs an O(n,n;Z)-invariant chiral-boson measure including the dilaton shift (1.5). §8 concedes the quantization of the self-duality constraint is open and lists the competing schemes [32-40]. So the abstract's 'are formulated' is a classical formulation; the n=1 check verifies the classical Buscher rules, not the measure. That is a genuine gap, but it is stated plainly and it is the right gap for a framework paper to leave. Footnote 1 is similarly honest about the T^3 H-flux example not being a CFT as it stands. Who should read it: anyone working on doubled geometry, generalized geometry, or non-geometric flux backgrounds — this is the conceptual ancestor of a lot of that. Worth a serious referee, and worth citing.

Referee report

Significance

If the construction holds, it converts a qualitative statement ('this background has no global geometry') into a precise one ('the local null T^n subspaces of the T^{2n} bundle do not glue into a global sub-bundle'), and it makes T-duality a statement about the choice of physical subspace rather than about a transformation of the background. That is a genuine conceptual advance and it organizes a large body of earlier examples (duality-twisted reductions, T-duals of flux compactifications, asymmetric orbifolds, mirrors of T^3-fibrations) under one geometric framework. The paper also earns credit for explicit internal checks rather than assertion: the n=1 case in section 3.1 is worked through and reproduces the standard Buscher rules (3.10)-(3.11), the reduction of the doubled lagrangian to the conventional sigma model is given in equations (2.45)-(2.50), and the product-structure characterization of polarizations in section 5 is a clean bijection rather than a heuristic. The construction contains no adjustable parameters and no fitted quantities; the only inputs are the O(n,n;Z) transition data and the coset form of H. The D-brane discussion in section 7 yields a concrete, check-1-

Major objections (2)

[§6, Eqs. (6.3)-(6.4); §8] The list of objects that are declared tensors on the doubled bundle ~M in (6.3)-(6.4) covers P, L, H and J, but not the dilaton. This matters because Eq. (1.5) shows that under an O(n,n;Z) transition function e^Φ picks up a factor (det G'/det G)^{1/4}, and det G is polarization-dependent, so Φ as defined is not a function on ~M. Since the abstract's central claim is that 'the global structure involves the doubled geometry', the paper should state explicitly what the dilaton is on ~M: for instance a section of a line bundle whose transition function is that determinant factor, or a shifted dilaton absorbing a determinant of the fibre metric, or a function on N only with the determinant factor attributed to the measure. As written, the reader cannot tell whether the doubled space carries the full background data or only the (H,J) part of it, and this is load-bearing for the global claim.
[§2.4, Eqs. (2.45)-(2.50)] The equivalence between the constrained doubled model and the standard sigma model is the bridge on which everything else rests, and it is asserted 'by an argument similar to that given in [27]' rather than shown. In particular, the claim that the Y-equations of the doubled lagrangian (2.3) with the constraint (2.5) reproduce the Y-equations of (2.48) with the identifications (2.49)-(2.50) is not verified in the text. A short explicit check, or at least a statement of which field equations were compared and how the k, v terms of (2.46) enter, would make the equivalence verifiable by the reader. The explicit n=1 treatment in section 3.1 partly compensates, but the general-n step is the one that carries the paper's claim.

Minor objections (9)

[Abstract] The abstract states that strings in T-fold backgrounds 'are formulated' in the enlarged space, whereas section 8 is explicit that the quantization of the constrained doubled model is open and that competing chiral-boson schemes [32-40] must still be shown to give a consistent, modular-invariant theory. The authors acknowledge this limitation, so the request is only that the abstract signal the classical/local character of the construction, for instance by saying that the backgrounds are 'described' or 'given a geometric formulation' locally.
[Abstract] The final sentence reads 'the physical D-brane is the part of the part of the physical space lying in the generalised D-brane subspace'; the duplicated 'part of the' should be removed.
[§4, Eq. (4.4) and §8] The symbol Φ is used both for the coset 'vielbein' converting O(n,n) indices to GL(n) indices in (4.4) and for the dilaton throughout. The text flags the clash parenthetically, but a distinct symbol for the coset representative (for example V or P, with the dilaton reserved for Φ) would remove an ambiguity that recurs in sections 4, 5 and 8.
[§3.2] The active/passive discussion describes the n=1 T-duality as 'rotating the vector through π/2' or 'rotating the axes through -π/2'. For n=1 the relevant group O(1,1;Z) is discrete, so the rotation language is only heuristic; saying that the discrete T-duality exchanges the two cycles of T^2, and that the two viewpoints differ in whether the exchange is applied to the geometry or to the polarization, would be more accurate without losing the intuition.
[§7, Eqs. (7.1)-(7.5)] The boundary conditions (7.1)-(7.2), the vanishing of the boundary term via (7.3), and the compatibility condition (7.4) with the self-duality constraint are stated without derivation, and the step from (7.4) to the normal form (7.5) is asserted. A sentence or two explaining why (7.4) is the correct compatibility condition, and why it forces the block form (7.5), would make section 7 self-contained.
[§1, p. 3] The phrase 'B is a gerb-connection' should read 'gerbe connection'; the same paragraph also uses 'gerbe connection' correctly, so the two spellings should be harmonized.
[§6 and §8] There are typographical errors that should be corrected: 'funcitons' in the sentence following (6.6), 'bane' in the sentence introducing the Dp_Y-brane in section 7, and 'somewehere' in the discussion of U-folds in section 8.
[References] Reference [30] (Floreanini and Jackiw, Phys. Rev. Lett. 59 (1987) 1873) duplicates reference [36] exactly; the two should be consolidated. References [23], [24] and [39] do not appear to be cited anywhere in the text and should either be cited or removed.
[§2.1, Eq. (2.3)] The world-sheet is taken flat at (2.3) and the Fradkin-Tseytlin term is deferred to section 8. A forward reference at (2.3) would spare the reader the impression that the coupling to world-sheet curvature has been overlooked, particularly since the dilaton transformation (1.5) is a measure effect.

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The paper

The paper claims

Hull proposes that string backgrounds glued together by T-duality, which have no global spacetime, are secretly ordinary manifolds once each torus fibre is doubled to carry both coordinates and their duals, with physical spacetime emerging,

The reading

The paper asks what a string background means when its coordinate patches are glued not by diffeomorphisms but by T-duality, the symmetry that trades a circle of radius $R$ for one of radius $1/R$. Hull's answer is to double the fibre: replace the local $n$-torus $T^n$ by a $T^{2n}$ carrying both the coordinates and their duals, on which the duality transition functions act as ordinary diffeomorphisms, and then impose a self-duality constraint that halves the doubled coordinates back to the right count of degrees of freedom. In the enlarged space the background is an honest manifold, and ordinary spacetime reappears only as a locally chosen null $T^n$ slice of each $T^{2n}$ fibre. The payoff is a sharp criterion: a background is geometric exactly when those local slices glue into a global $T^n$ sub-bundle, and non-geometric when they do not, so that 'non-geometric' stops being a slogan and becomes a statement about the topology of the doubled bundle.

What carries the argument

The load-bearing device is the doubled $\sigma$ model: a world-sheet Lagrangian $L_d = -1/2 H_{IJ} P^I /wedge *P^J + P^I /wedge *J_I + L(Y)$ in which the $2n$ one-form momenta $P^I$ on $T^{2n}$ obey $dP^I = 0$ and are subject to the self-duality constraint above, with $H$ a positive-definite metric on $T^{2n}$ built from a vielbein of $O(n,n)/(O(n) times O(n))$ so that it is parameterised by the usual $n$-torus metric and $B$-field, $E = G + B$. Solving the constraint for $n$ of the coordinates reproduces the standard Buscher $\sigma$-model, which is how the formalism is checked against known T-duality rules. The second device is the polarization, encoded as an integral product structure $R in GL(2n;Z)$ with $R^2 = 1$, whose $+1$ and $-1$ eigenspaces are the physical $T^n$ and the dual $tilde{T}^n$; the three structures $R$, $S = LH$ and $I = SR$ satisfy an $SL(2,R)$ algebra, and the subgroup of $O(n,n)$ preserving all three is $O(n)$. This is what makes 'choosing a spacetime' a precise, local, and generally non-integrable operation.

Extended reading notes

Core claim

The central claim is that a T-fold, a background whose fibres are locally $n$-tori and whose transition functions lie in $O(n,n;Z)$ rather than in the geometric subgroup $GL(n;Z)$, can be reformulated as a string propagating on a genuine $T^{2n}$ bundle over the same base, subject to a self-duality constraint on the doubled momenta. The constraint, $P^I = L^{IJ} * (H_{JK}P^K + J_J)$ with $S^2 = 1$ for $S = LH$, is the covariant generalisation of the statement that half the doubled coordinates are left-movers and half are right-movers, with the split itself depending on position in the base. Choosing a physical spacetime then amounts to choosing a polarization: a maximal null $T^n$ subspace of each $T^{2n}$ fibre, equivalently an integral product structure $R$ with $R^2 = 1$ that is pseudo-hermitian with respect to the $O(n,n)$ metric. T-duality acts by changing that choice rather than by changing the background, and the physics is asserted to be independent of it. For a geometric background the locally chosen $T^n$ slices fit together into a $T^n$ bundle over the base; for a T-fold they do not, and there is a doubled manifold but no spacetime manifold.

Load-bearing premise

The whole construction is a classical $\sigma$-model rewriting, and it describes strings only if the self-duality constraint $P^I = L^{IJ} * (H_{JK}P^K + J_J)$ can be imposed consistently in the quantum theory; the paper concedes in its discussion that this is unresolved, pointing to competing chiral-boson quantization schemes and to the cancellation of conformal and Lorentz anomalies and to modular invariance as outstanding requirements.

Editorial extensions

If this is right

T-duality becomes a passive operation: instead of transforming the background fields by the Buscher rules, one keeps the doubled geometry fixed and rotates the polarization, and the statement that the physics is T-duality invariant becomes the statement that no polarization is preferred.
For open strings, a generalized D-brane wraps a null $T^n$ of each $T^{2n}$ fibre, and the physical D-brane is the intersection of that Dirichlet subspace with the physical slice, so a $Dp$-brane in one patch can be glued to a $Dp'$-brane with $p' \neq p$ in an overlapping patch.
Compactification on a T-fold still yields an ordinary low-energy field theory on the base, even in cases where no field-theory description exists on the total space.
The construction extends formally to transition functions in U-duality, mirror symmetry, and to M-theory, where the doubled torus is enlarged to include coordinates conjugate to membrane, fivebrane, and Kaluza-Klein-monopole wrapping charges.
The $n=1$ case shows the mechanism concretely: gluing a circle of radius $R$ to one of radius $1/R$ produces a smooth doubled $T^2$ bundle whose physical $S^1$ sub-bundle does not exist globally.

Reading between the lines

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

If 'non-geometric' means 'the local polarizations fail to glue', then the failure should be measurable by a cohomology class on the base, and different non-geometric flux backgrounds ought to be distinguishable by that class rather than only by their local field content.
Because the doubled total space is a genuine manifold with a genuine $O(n,n;Z)$ bundle structure, standard topological tools, characteristic classes and index theorems, become available for non-geometric backgrounds that had none before; that seems the most direct route to invariants of T-folds.
The identification of a polarization with a pure spinor of $Spin(n,n)$ suggests that generalized complex and generalized Kähler geometry, developed for the geometric case, may classify which polarizations are admissible and which obstructions are possible.
A natural check outside the paper's scope is whether the doubled description survives when the fibre is not a torus: if the mechanism is really about null subspaces and self-duality, some analogue should exist for Calabi-Yau or K3 fibrations, and if none does, the construction is more tied to tori than the discussion implies.

Original abstract

A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirrors of flux compactifications, from reductions with duality twists and from asymmetric orbifolds. Strings in ` T-fold' backgrounds with a local $n$-torus fibration and T-duality transition functions in $O(n,n;\Z)$ are formulated in an enlarged space with a $T^{2n}$ fibration which is geometric, with spacetime emerging locally from a choice of a $T^n$ submanifold of each $T^{2n}$ fibre, so that it is a subspace or brane embedded in the enlarged space. T-duality acts by changing to a different $T^n$ subspace of $T^{2n}$. For a geometric background, the local choices of $T^n$ fit together to give a spacetime which is a $T^n$ bundle, while for non-geometric string backgrounds they do not fit together to form a manifold. In such cases spacetime geometry only makes sense locally, and the global structure involves the doubled geometry. For open strings, generalised D-branes wrap a $T^n$ subspace of each $T^{2n}$ fibre and the physical D-brane is the part of the part of the physical space lying in the generalised D-brane subspace.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,901 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.23 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirrors of flux compactifications, from reductions with duality twists and from asymmetric orbifolds. Strings in ` T-fold' backgrounds with a local $n$-torus fibration and T-duality transition functions in $O(n,n;\Z)$ are formulated in an enlarged space with a $T^{2n}$ fibration which is geometric, with spacetime emerging locally from a choice of a $T^n$ submanifold of each $T^{2n}$ fibre, so that it is a subspace or brane embedded in the enlarged space. T-duality acts by changing to a different $T^n$ subspace of $T^{2n}$. For a geometric background, the local choices of $T^n$ fit together to give a spacetime which is a $T^n$ bundle, while for non-geometric string backgrounds they do not fit together to form a manifold. In such cases spacetime geometry only makes sense locally, and the global structure involves the doubled geometry. For open strings, generalised D-branes wrap a $T^n$ subspace of each $T^{2n}$ fibre and the physical D-brane is the part of the part of the physical space lying in the generalised D-brane subspace.

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	A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations.	background 0.97	0.11	0.18	asserted 1.00
s1	Non-geometric string backgrounds arise from T-duals and mirrors of flux compactifications, from reductions with duality twists and from asymmetric orbifolds.	background 1.00	0.08	0.06	asserted 1.00
s2	Strings in ` T-fold' backgrounds with a local $n$-torus fibration and T-duality transition functions in $O(n,n;\Z)$ are formulated in an enlarged space with a $T^{2n}$ fibration which is geometric, with spacetime emerging locally from a choice of a $T^n$ submanifold of each $T^{2n}$ fibre, so that it is a subspace or brane embedded in the enlarged space.	contribution 0.57	0.41	0.37	asserted 1.00
s3	T-duality acts by changing to a different $T^n$ subspace of $T^{2n}$.	interpretation 0.45	0.28	0.09	asserted 1.00
s4	For a geometric background, the local choices of $T^n$ fit together to give a spacetime which is a $T^n$ bundle, while for non-geometric string backgrounds they do not fit together to form a manifold.	interpretation 0.51	0.32	0.25	asserted 1.00
s5	In such cases spacetime geometry only makes sense locally, and the global structure involves the doubled geometry.	interpretation 0.93	0.26	0.22	asserted 1.00
s6	For open strings, generalised D-branes wrap a $T^n$ subspace of each $T^{2n}$ fibre and the physical D-brane is the part of the part of the physical space lying in the generalised D-brane subspace.	contribution 0.38	0.33	0.11	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.63 · evidence from argument 0.64.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

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Generalised Geometry for M-Theory
hep-th 2007-01 conditional novelty 8.0 of 10

The paper builds exceptional generalised geometries, replacing SO(d,d) with E_n for M-theory and E_{d+1} for type II strings, so that metric, 3-form and Ramond-Ramond flux sit inside one bundle.
Worldsheet CFTs for Flat Monodrofolds
hep-th 2006-04 conditional novelty 8.0 of 10

A new wilsonization construction produces modular-invariant worldsheet CFTs for flat monodrofolds, with momentum fractionated in units of 1/N^2, and yields a new 7D N=1 type II vacuum.

Show 55 more citing papers

Topological Effects in Neural Network Field Theory
hep-th 2026-04 unverdicted novelty 7.0 of 10

Neural network field theory extended with discrete topological labels recovers the BKT transition and bosonic string T-duality.
$L_\infty$-algebraic extensions of non-Lorentzian kinematical Lie algebras, gravities, and brane couplings
hep-th 2025-12 unverdicted novelty 7.0 of 10

L_infinity extensions of Galilean, Newton-Hooke and static algebras produce infinite towers of p-form fields that couple to torsionful non-Lorentzian gravities and yield WZW terms for (p-1)-branes via doubled coordinates.
Cobordism Utopia: U-Dualities, Bordisms, and the Swampland
hep-th 2025-05 conditional novelty 7.0 of 10

For 8d maximal supergravity, the spin bordism groups Omega_k^Spin(B(SL(2,Z) x SL(3,Z))) for k=1..7 are computed and each generator is realized by a string/M/F-theory background, some of which are non-geometric.
Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields
hep-th 2019-09 accept novelty 7.0 of 10

Mixed-symmetry potentials such as the dual graviton are embedded into exceptional field theory's p-form multiplets, with T- and S-duality rules derived for the E8 case.
S-folds and 4d N=3 superconformal field theories
hep-th 2016-02 accept novelty 7.0 of 10

Only five variants of N=3-preserving S-folds exist, labeled by (k,ell) = (3,1), (3,3), (4,1), (4,4), (6,1), as shown by matching F-theory discrete torsion against M-theory orbifold charges.
Metastring Theory and Modular Space-time
hep-th 2015-02 conditional novelty 7.0 of 10

Requiring worldsheet locality and modular invariance in a chiral phase-space string forces a unique self-dual Lorentzian lattice, which the authors reinterpret as a quantum 'modular space-time' rather than an ordinary...
Double Field Theory on Group Manifolds
hep-th 2014-10 conditional novelty 7.0 of 10

A cubic-order double field theory is derived for WZW group-manifold backgrounds, with a background-dependent covariant derivative and a new strong constraint that closes the gauge algebra even for left-right asymmetri...
Large Gauge Transformations in Double Field Theory
hep-th 2012-07 conditional novelty 7.0 of 10

Finite gauge transformations in double field theory can be written as generalized coordinate transformations whose composition follows the Courant bracket and is non-associative on coordinates.
Supergravity as Generalised Geometry I: Type II Theories
hep-th 2011-07 accept novelty 7.0 of 10

Type II supergravity is reformulated as a generalised geometry with an O(9,1)xO(1,9) structure, giving a generalised Levi-Civita connection and curvature that reproduce the action, equations of motion and supersymmetr...
Stringy differential geometry, beyond Riemann
hep-th 2011-05 conditional novelty 7.0 of 10

A single geometric framework treats the metric, B-field, and dilaton on equal footing and rewrites the closed-string low-energy action as one term, with O(D,D) T-duality and double-gauge symmetry manifest.
The gauge algebra of double field theory and Courant brackets
hep-th 2009-08 accept novelty 7.0 of 10

For fields restricted to a null subspace, the gauge algebra of double field theory closes with field-independent structure constants and its bracket is exactly the Courant bracket of generalized geometry.
Monodromy in the CMB: Gravity Waves and String Inflation
hep-th 2008-03 conditional novelty 7.0 of 10

Monodromy of a D4-brane on a Nil manifold yields a phi^(2/3) inflaton potential, predicting ns around 0.98 and r around 0.04, a testable gravitational-wave signature from string theory.
Flux Compactifications of M-Theory on Twisted Tori
hep-th 2006-03 conditional novelty 7.0 of 10

The bosonic sector of gauged supergravities from M-theory on twisted tori with flux is derived for arbitrary dimension, with conditions for a full compactification and a check of equivalence to universal gauged superg...
Generalized N=1 Orientifold Compactifications and the Hitchin functionals
hep-th 2006-02 conditional novelty 7.0 of 10

The paper derives N=1 Kähler potentials and superpotentials for type II orientifolds on SU(3)-structure manifolds and proposes generalized half-flat manifolds as mirrors of Calabi-Yau compactifications with NS-NS flux.
More Dual Fluxes and Moduli Fixing
hep-th 2006-02 conditional novelty 7.0 of 10

Adding a new set of S-dual non-geometric fluxes to type IIB orientifolds yields N=1 Minkowski vacua in which the dilaton, complex structure, and Kahler moduli are all fixed.
Generalised T-Duality and Non-Geometric Backgrounds
hep-th 2005-12 conditional novelty 7.0 of 10

The paper identifies a new class of non-geometric string backgrounds with dependence on dual (winding) coordinates and argues that a generalised T-duality maps flux compactifications and T-folds onto them.
Nongeometric Flux Compactifications
hep-th 2005-08 accept novelty 7.0 of 10

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.
Duality-covariant particles and exotic branes
hep-th 2026-06 unverdicted novelty 6.0 of 10

Proposes enlarged worldline models with coadjoint orbit terms and generalized worldvolume theories for exotic branes that make E8 duality covariance manifest in a Hamiltonian formulation.
Gauged Extended Field Theory and Generalised Cartan Geometry
hep-th 2025-09 conditional novelty 6.0 of 10

A systematic Cartan-geometric construction of linearised torsion and curvature hierarchies for generalised geometries with global duality group G and local gauge group H, realised via brane current algebras.
Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
hep-th 2019-08 conditional novelty 6.0 of 10

The gauge structure and pseudo-action of extended geometry with ancillary transformations are encoded by a tensor hierarchy algebra S(g+), yielding a partial L-infinity description for finite-dimensional structure groups.
Special Holonomy Manifolds, Domain Walls, Intersecting Branes and T-folds
hep-th 2019-08 conditional novelty 6.0 of 10

The Gibbons-Lu-Pope-Stelle special holonomy domain wall metrics are T-dual to intersecting brane systems, yielding new multi-function special holonomy metrics and T-fold backgrounds.
Type II DFT solutions from Poisson-Lie T-duality/plurality
hep-th 2019-03 conditional novelty 6.0 of 10

A general O(D,D) transformation rule for Ramond-Ramond fields under non-Abelian T-duality and Poisson-Lie T-plurality is derived, and the dilaton puzzle is resolved using double field theory.
Holographic duals of 3d S-fold CFTs
hep-th 2018-04 accept novelty 6.0 of 10

A class of non-geometric AdS4 string backgrounds is shown to match the three-sphere partition function of a proposed dual 3d N=4 quiver theory, exactly at finite N and in the large-N gravity limit.
Asymptotically-flat supergravity solutions deep inside the black-hole regime
hep-th 2017-11 conditional novelty 6.0 of 10

Smooth asymptotically-flat supergravity solutions with the same charges as D1-D5-P black holes are constructed, with arbitrarily small angular momentum and identified dual CFT states.
Classification of non-Riemannian doubled-yet-gauged spacetime
hep-th 2017-07 accept novelty 6.0 of 10

Every non-Riemannian Double Field Theory background is classified by two integers (n, n̄), with Newton-Cartan, Carroll, and Gomis-Ooguri geometries appearing as special cases.
Half-maximal supersymmetry from exceptional field theory
hep-th 2017-07 conditional novelty 6.0 of 10

Half-maximal warped AdS and Minkowski vacua of type II and 11-dimensional supergravity always admit a consistent truncation keeping only the gravitational supermultiplet, proved via exceptional generalised SO(d-1) str...
Generalised Kinematics for Double Field Theory
hep-th 2017-06 conditional novelty 6.0 of 10

A canonical connection on a para-Hermitian manifold yields a generalized Lie derivative whose symmetry algebra closes for curved O(d,d) metrics, and this construction is isomorphic to Generalized Geometry on the integ...
Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
hep-th 2017-05 conditional novelty 6.0 of 10

Homogeneous Yang-Baxter deformations of string backgrounds are shown, for the cases checked, to be beta-field twists realizable as generalized diffeomorphisms in double field theory.
Weyl invariance for generalized supergravity backgrounds from the doubled formalism
hep-th 2017-03 conditional novelty 6.0 of 10

The generalized supergravity equations and the Weyl invariance of the bosonic string on such backgrounds follow from ordinary double field theory with a dilaton that depends linearly on dual coordinates.
Extended Riemannian Geometry I: Local Double Field Theory
hep-th 2016-11 accept novelty 6.0 of 10

A graded-manifold framework called extended Riemannian geometry reproduces double field theory's symmetries and yields a coordinate-invariant form of its strong section condition.
New gaugings and non-geometry
hep-th 2015-06 accept novelty 6.0 of 10

The omega-deformed SO(8) gauged supergravities admit no locally geometric uplift to eleven- or ten-dimensional supergravity, and the section-violating frames that do reproduce their gauge algebra fail global quantisat...
Consistent Kaluza-Klein Truncations via Exceptional Field Theory
hep-th 2014-10 accept novelty 6.0 of 10

Explicit twist matrices in exceptional field theory generate consistent Kaluza-Klein truncations of M-theory and type IIB onto spheres and warped hyperboloids, with gauge groups SO(p,q) and CSO(p,q,r).
Branes are Waves and Monopoles
hep-th 2014-09 conditional novelty 6.0 of 10

The M5-brane and the NS5-brane appear as Kaluza-Klein monopole solutions of exceptional extended geometry and double field theory, extending the earlier identification of branes as null waves.
Effective actions of non-geometric fivebranes
hep-th 2013-09 conditional novelty 6.0 of 10

The type IIB 5^2_2 and 5^3_2 exotic fivebranes are shown, via T- and S-duality chains, to couple to mixed-symmetry dual potentials and to source non-geometric Q and Ramond-Ramond P fluxes.
Covariant action for a string in doubled yet gauged spacetime
hep-th 2013-07 accept novelty 6.0 of 10

The coordinate gauge symmetry of doubled spacetime is equivalent to the section condition, and a gauge connection built on this principle yields a string action covariant under all relevant symmetries, including for d...
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.
Gauged Linear Sigma Model for Exotic Five-brane
hep-th 2013-04 conditional novelty 6.0 of 10

A new T-duality transformation of an N=(4,4) gauged linear sigma model, applied even in the presence of F-terms, produces a worldsheet theory whose infrared limit is the exotic 5^2_2-brane with B-field.
(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.
Incorporation of fermions into double field theory
hep-th 2011-09 conditional novelty 6.0 of 10

Fermions can be incorporated into double field theory in a fully T-duality-covariant way, and a T-duality rotation flips their chirality exactly when a background-dependent determinant equals minus one.
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...
String Solitons and T-duality
hep-th 2011-02 conditional novelty 6.0 of 10

A universal T-duality-covariant Wess-Zumino term is constructed for supersymmetric string solitons in any dimension, and the surviving branes are identified as lightlike conjugacy classes inside antisymmetric tensor r...
Generalized Geometry and M theory
hep-th 2010-08 conditional novelty 6.0 of 10

The Hamiltonian of bosonic eleven-dimensional supergravity can be recast in terms of a single generalized metric with manifest SL(5) symmetry, with no dimensional reduction, provided fields are taken independent of du...
Generalized metric formulation of double field theory
hep-th 2010-06 accept novelty 6.0 of 10

The double field theory action and its gauge transformations are recast in terms of the O(D,D) generalized metric, making T-duality manifest and identifying the gauge algebra with a doubled Courant bracket.
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...
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.
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...

See all 87 Pith citations

How later papers used it

231 later papers cite it

Evidence: substantial. 223 of the citing papers share no author with it, and 16 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 490 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

5 later papers by other authors are listed below: 2 built on it, 2 used its method or tool and 1 compared its own results with it. 1 more paper by the same authors is listed: 1 built on it.

Builds on it 3 of 8 papers with this label · 1 by the same authors

Extended the notions introduced in this paper to understand the meaning of changing polarization in the framework of para-Hermitian geometry.

Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds (2018) · 0.95 · paraphrased: the licence does not allow quoting
Further enlarged the possibilities considered in this paper, overcoming some obstacles encountered in another work for the flat group example.

Worldsheet theories for non-geometric string backgrounds (2008) · 0.93 · paraphrased: the licence does not allow quoting

By the same authors

Systematically investigated the generalisation of the doubled formalism of this paper to the doubled twisted torus G/Γ for general groups G with a natural metric of signature (D,D).

Non-geometric backgrounds, doubled geometry and generalised T-duality (2009) (same authors) · 0.95 · paraphrased: the licence does not allow quoting

Uses its method or tool 2 of 7 papers with this label

Doubled the internal T^4 coordinates as in this paper by introducing dual coordinates for a dual torus conjugate to the winding modes wrapping the cycles of T^4.

N=4 Gauged Supergravity from Duality-Twist Compactifications of String Theory (2008) · 0.99 · paraphrased: the licence does not allow quoting
Used the form most recently championed by Hull in this paper as its starting point.

Background Field Equations for the Duality Symmetric String (2007) · 0.97 · paraphrased: the licence does not allow quoting

Compares with it 1 of 6 papers with this label

Used another work to compare the results of this paper with C*-algebraic topological T-duality.

Topological T-duality and T-folds (2008) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

217 arXiv papers cite this in 470 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 · 279 sentences without a confident label

Builds on it 8 papers

In this paper we systematically investigate the generalisation of the doubled formalism of [ref] to the doubled twisted torus $G /Γ$ for general groups $G$ that have a natural metric of signature $(D,D)$.

Non-geometric backgrounds, doubled geometry and generalised T-duality · Introduction · 0.95
This overcomes some obstacles encountered in [ref] for the flat group example and further enlarges the possibilities considered in [ref] .

Worldsheet theories for non-geometric string backgrounds · Introduction · 0.93
We also consider the sigma model introduced in [ref] on the doubled space which generalises the sigma model of [ref] and overcomes the deficiencies of the sigma model of [ref] by allowing the inclusion of $H$- and $R$-fluxes.

Bi-algebras, generalised geometry and T-duality · Doubled Geometry · 0.91

Uses its method or tool 7 papers

In the language of [ref] , the doubled Lagrangian is [equation] The two fiber coordinates are collectively labeled $^I = (θ, )$ with positive definite fiber metric $_IJ$ and connection 1-form components $^I_a = ^I_m ∂_a r^m$. $L_IJ = ([ 0 1; 1 0 ])$ is an $O(1,1)$ invariant metric on the fibers; its inverse is $L^IJ$. $(r^m)$ gives the sigma model on the base space.

The KK-Monopole/NS5-Brane in Doubled Geometry · The doubled monopole action · 0.81
We will use the form most recently championed by Hull [ref] as our starting point.

Background Field Equations for the Duality Symmetric String · Introduction · 0.97
In this paper we will follow the approach of Hull [ref] and eliminate the dual coordinates by a gauging procedure.

The Exceptional Sigma Model · Background · 0.99

Compares with it 6 papers

We use the work of Echterhoff, Nest and Oyono-Oyono [ref] to compare the results of Ref. [ref] with $C^∗$-algebraic topological T-duality.

Topological T-duality and T-folds · A Topological Approximation of $H$-flux · 0.99
A similar construction was seen for the doubled torus bundle in [ref] .

Flux compactifications, twisted tori and doubled geometry · Choosing a polarisation and gauging the sigma model · 0.80
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 1 paper

However, as shown in [ref] , this space can be promoted to a global background if in addition to diffeomorphisms one considers T-duality transformations as transition functions.

T-duality revisited · T-duality along $k_(2)$ · 0.97

Cites it as background 131 papers

The doubled formalism was described by Hull in [ref] and drew from previous duality covariant models [ref] .

Aspects of M-Theory Brane Interactions and String Theory Symmetries · Introducing the Formalism · 0.93
Doubled geometry in its current form was introduced by Hull in [ref] : by making the T-duality of string theory manifest one is able to describe non-geometric string backgrounds not accessible in conventional formulations.

The KK-Monopole/NS5-Brane in Doubled Geometry · The doubled monopole action · 0.97
In [ref] Hull formulated a sigma model with a target it space which is a torus fibration (some earlier related work can be found in [ref] ).

Connecting T-duality invariant theories · Introduction · 0.90

Discussion

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