T-duality for principal torus bundles and dimensionally reduced Gysin sequences

Bouwknegt, Peter; Hannabuss, K. C.; Mathai, Varghese

doi:10.4310/atmp.2005.v9.n5.a4

Cited by 48 publications

(96 citation statements)

References 28 publications

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“…In particular, for n = 2 (hereafter called non-geometric Q-flux background), T-dualities can induce fuzziness, apart from topology change, leading to non-commutative tori in closed string compactifications [3][4][5], whereas for n ≥ 3 (the non-geometric R-flux background) the situation becomes even more interesting as non-geometric closed string backgrounds attached to non-associative tori come into play [6,7]. Similar results based on somewhat less explicit methods appeared in the literature before [8][9][10][11][12][13][14], while studying the action of T-duality on torus fibrations with fluxes.…”

Section: Jhep01(2014)171mentioning

confidence: 76%

3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua

Bakas

Lüst

2014

J. High Energ. Phys.

134

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Abstract:We consider the geometric and non-geometric faces of closed string vacua arising by T-duality from principal torus bundles with constant H-flux and pay attention to their double phase space description encompassing all toroidal coordinates, momenta and their dual on equal footing. We construct a star-product algebra on functions in phase space that is manifestly duality invariant and substitutes for canonical quantization. The 3-cocycles of the Abelian group of translations in double phase space are seen to account for non-associativity of the star-product. We also provide alternative cohomological descriptions of non-associativity and draw analogies with the quantization of point-particles in the field of a Dirac monopole or other distributions of magnetic charge. The magnetic field analogue of the R-flux string model is provided by a constant uniform distribution of magnetic charge in space and non-associativity manifests as breaking of angular symmetry. The Poincaré vector comes to rescue angular symmetry as well as associativity and also allow for quantization in terms of operators and Hilbert space only in the case of charged particles moving in the field of a single magnetic monopole.

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Section: Jhep01(2014)171mentioning

confidence: 76%

3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua

Bakas

Lüst

2014

J. High Energ. Phys.

134

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“…What also remains to be done is T-duality for nonabelian principal bundles, where some of the ideas of this paper and [5] apply.…”

Section: Applications To T-dualitymentioning

confidence: 99%

“…[18,5] for more details). [The conclusions in this paper are valid for integral classes H ∈ H 3 (E, Z) as well, since this paper deals exclusively with the introduction of the additional 'degree of freedom' H 0 , which does not carry torsion, on top of established results which hold in the case of torsion H. Note that H 0 can be identified with the restriction of H to a fibre.…”

Section: Introductionmentioning

confidence: 99%

“…This would then enable one to give a more symmetric characterization the T-dual, similar to part (1) of the Theorem above. We have an explicit conjecture for this, the explanation for which is in [5], namely, for the continuous field of noncommutative tori A f , there should be a "Chern class" invariant c 1 (A f ) = (H 2 , H 1 , 0) satisfying dH 2 + c 1 (E) ∧ H 1 = 0. In this case, we can add the following to part (2) of the Theorem above.…”

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confidence: 99%

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Nonassociative Tori and Applications to T-Duality

Bouwknegt

Hannabuss²,

Mathai

2006

Commun. Math. Phys.

Self Cite

118

229

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Abstract. In this paper, we initiate the study of C * -algebras A endowed with a twisted action of a locally compact Abelian Lie group G, and we construct a twisted crossed product A⋊G, which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed product algebra are studied in detail, and are applied to T-duality in Type II string theory to obtain the T-dual of a general principal torus bundle with general H-flux, which we will argue to be a bundle of noncommutative, nonassociative tori. We also show that this construction of the T-dual includes all of the special cases that were previously analysed.

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“…Presumably there should be some analog of twisted K-theory for the general flat fiber theories that we are studying, including also the non-geometric fluxes. Matching this onto the work of Mathai and collaborators [46,47,48,49,50,35,51,52] would be very interesting. Similarly, exploiting the connections between the base-fiber approach described here and spaces with generalized complex structure (see e.g.…”

Section: Advantages and Puzzlesmentioning

confidence: 99%

Toroidal orientifolds in IIA with general NS-NS fluxes

Ihl

Robbins

Wrase

2007

J. High Energy Phys.

184

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Type IIA toroidal orientifolds offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NS-NS and R-R field strengths, but also fluxes that are T-dual to the NS-NS three-form flux. These new ingredients are known as metric fluxes and non-geometric fluxes, and can help stabilize moduli or can lead to other new features. In this paper we study two approaches to these constructions, by effective field theory or by toroidal fibers twisted over a toroidal base. Each approach leads us to important observations, in particular the presence of D-terms in the four-dimensional effective potential in some cases, and a more subtle treatment of the quantization of the general NS-NS fluxes. Though our methods are general, we illustrate each approach on the example of an orientifold of T 6 /Z 4 .

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T-duality for principal torus bundles and dimensionally reduced Gysin sequences

Cited by 48 publications

References 28 publications

3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua

3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua

Nonassociative Tori and Applications to T-Duality

Toroidal orientifolds in IIA with general NS-NS fluxes

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