T-duality with H-flux: non-commutativity, T-folds and G x G structure

Pascal Grange; Sakura Schafer-Nameki

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T-duality with H-flux: non-commutativity, T-folds and G x G structure

Pascal Grange, Sakura Schafer-Nameki

High Energy Physics - Theory · Submitted 12 Sep 2006

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The authors' main claim Various approaches to T-duality with NSNS three-form flux are reconciled.

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arXiv IDhep-th/0609084 (version 2)

Pith ID74KLC4PW, Pith's permanent record of this paper and its review

CitationPascal Grange, Sakura Schafer-Nameki. "T-duality with H-flux: non-commutativity, T-folds and G x G structure." arXiv:hep-th/0609084 (2006). https://pith.science/paper/74KLC4PW

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

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Various approaches to T-duality with NSNS three-form flux are reconciled.	contribution 0.72	0.77	0.15	asserted 0.99
s1	Non-commutative torus fibrations are shown to be the open-string version of T-folds.	result 0.92	0.84	0.27	asserted 1.00
s2	The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds.	contribution 0.63	0.87	0.25	asserted 1.00
s3	The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy.	result 0.95	0.78	0.20	asserted 1.00
s4	This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds.	result 0.76	0.46	0.13	asserted 0.94
s5	The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector.	result 0.85	0.65	0.11	asserted 0.93
s6	Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors.	result 0.98	0.91	0.17	hedged possibility 0.92

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Original abstract

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors.

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Cited by 12 Pith papers

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

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20 arXiv papers cite this in 29 sentences

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Papers citing it · 17 sentences without a confident label

Builds on it 1 paper

To this end, we revisit the problem of formulating effective noncommutative Yang–Mills theories on D-branes in non-geometric tori in the decoupling limit, extending the earlier work of [ref] (see also [ref] ) in various directions.

Noncommutative gauge theories on D-branes in non-geometric backgrounds · Introduction and summary · 1.00

Cites it as background 10 papers

D-branes in non-geometric backgrounds were previously discussed from the point of view of doubled (twisted) torus geometry in [ref] , directly in string theory from a target space perspective in [ref] , and from open string worldsheet theory in [ref] .

Noncommutative gauge theories on D-branes in non-geometric backgrounds · Introduction and summary · 0.91
It has been known for a some time that string theories may be defined on backgrounds which are not conventional geometries (See Refs. [ref] and references therein).

Topological T-duality and T-folds · Introduction · 0.99
More complete pictures of these dualities in the presence of fluxes have appeared once manifolds with $SU(3) ×SU(3)$ structure [ref] - [ref]

Heterotic type IIA duality with fluxes - towards the complete story · Introduction · 0.86

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