NS-NS fluxes in Hitchin's generalized geometry

Ian Ellwood

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NS-NS fluxes in Hitchin's generalized geometry

Ian Ellwood

High Energy Physics - Theory · Submitted 12 Dec 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.22 · mentions code or data availability 0.01.

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The standard notion of NS-NS 3-form flux is lifted to Hitchin's generalized geometry. This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux. Finally, a generalized connection that acts on generalized vectors is described and we show how the flux arises from it.

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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	The standard notion of NS-NS 3-form flux is lifted to Hitchin's generalized geometry.	contribution 0.99	0.78	0.16	asserted 1.00
s1	This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle.	method 0.64	0.79	0.15	asserted 1.00
s2	Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux.	result 0.94	0.95	0.58	asserted 1.00
s3	Finally, a generalized connection that acts on generalized vectors is described and we show how the flux arises from it.	contribution 0.87	0.91	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.85 · evidence from proof or derivation 1.00.

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arXiv listing abstract v4

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The paper

Original abstract

The standard notion of NS-NS 3-form flux is lifted to Hitchin's generalized geometry. This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux. Finally, a generalized connection that acts on generalized vectors is described and we show how the flux arises from it.

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References

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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...
Branes on Poisson varieties
math.DG 2007-10 accept novelty 7.0 of 10

Generalized connections on Courant algebroids give a new characterization of generalized Kähler geometry and an explicit construction of generalized Kähler structures on Poisson Fano manifolds.
A Unique Connection for Born Geometry
hep-th 2018-06 accept novelty 6.0 of 10

A Born geometry admits a unique torsion-free connection preserving its metric, symplectic form, and generalized metric, extending the Levi-Civita theorem to double field theory.
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...
Toroidal Orientifolds in IIA with General NS-NS Fluxes
hep-th 2007-05 conditional novelty 6.0 of 10

Metric fluxes in Type IIA toroidal orientifolds generate D-terms in the four-dimensional potential, and the quantization of general NS-NS fluxes is not the naive integer condition.

Show 3 more citing papers

SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
hep-th 2006-12 conditional novelty 6.0 of 10

SU(3)xSU(3) structure compactifications provide the mirror dual of Calabi-Yau compactifications with magnetic H-flux, with a new dual flux parameter completing the mirror map.
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.
Non-geometric backgrounds in string theory
hep-th 2018-11 accept

The review maps how T-duality, generalised geometry, and flux compactifications describe string backgrounds that cannot be given an ordinary Riemannian geometry.

How the literature uses it

16 arXiv papers cite this in 24 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 · 14 sentences without a confident label

Builds on it 2 papers

Our definitions will follow closely those in [ref] though, in connecting to supergravity, it is important to extend the definitions to include the $^+$ factor in the generalised structure bundle.

Supergravity as Generalised Geometry I: Type II Theories · Generalised $O(d,d)×^+$ connections and torsion · 0.96
In this example, we generalize the (generalized) Bismut connection from the case $p=1$, whose significance in the context of generalized geometry was first understood and investigated in [ref] .

Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions · Introduction · 0.95

Compares with it 1 paper

The generalized Bismut connection in this case is same as the one in [ref] .

Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions · Torsion operator · 1.00

Cites it as background 6 papers

discussed briefly in appendix A of [ref] based on the language of [ref] .

Quantization of charges and fluxes in warped Stenzel geometry · $SL(2,Z)$ dual of $TN ×S^1$ · 0.91
The notion of connection on a Courant algebroid was first introduced by Alekseev and Xu [ref] and Gualtieri [ref] , as well as Ellwood [ref] .

Supergravity as Generalised Geometry I: Type II Theories · Generalised $O(d,d)×^+$ connections and torsion · 0.95
The most developed one being double field theory (DFT) [ref] which postulates that the effective description of strings compactified on torii of radius $R$ is in terms of fields that live in a doubled space.

A Unique Connection for Born Geometry · Introduction · 0.95

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